9
CHAPTER 3 -- METHODS OF ANALYSIS
Task 1: Formulate Drought Scenarios
This task assessed the probability of severe drought and developed drought scenarios for the
major water resource systems of the study area. Scenarios were developed for the 50 and 100-year return
period droughts. The 1950s drought was also replicated, an event still significant in minds of many
current senior water managers today.
These drought scenarios were characterized from gaged historical flow records of the Rio
Grande and its tributaries. Fairly complete flow data along the river is available for the past 100 years.
Drought scenarios for the analysis proposed here were developed under the supervision of Dr. Phil King
with assistance by Mr. Brad Dixon who completed his masters degree in summer 2000 at New Mexico
State University’s Department of Civil, Agricultural, and Geological Engineering.
First, based on time series analysis of the existing flow data, synthetic drought scenarios of a
given return period were formulated using methods similar to those developed for the Colorado Basin
drought study (Tarboten 1995). The Colorado Basin study, modeled with independent annual flows,
autoregression order one with fixed parameters, autoregressive order one with uncertain parameters, and
fractional Gaussian noise modeling, used the estimated Hurst coefficient. While the existing data for the
Rio Grande Basin only covers a 100-year period, it appears that severe and sustained drought with
significant impact on the area's population has a return period in that order of magnitude. Extrapolation
to longer return period droughts through dendrohydrology or other indirect methods appeared
unnecessary.
Second, statistical analysis was used following established hydrologic principles (e.g., Benjamin
and Cornell 1970; Hann 1977). The drought of the late 1950s was very severe. Farmers responded by
installing wells and supplementing their surface water with groundwater. Since that time, competition for
10
water has increased considerably. An evaluation of that drought scenario on current water users was
conducted. In order to put the drought into perspective, its return period was calculated from the
statistical analysis performed as described above.
Task 2: Formulate a Hydrology-Institutions Model of the Rio Grande Basin
The aim of this task was to develop a hydrologic-institutions component to the overall model that
accounts for major sources and uses of water in the Rio Grande Basin. Water use patterns throughout the
basin will be altered as supplies are reduced due to drought.
This component accounts for institutional response under present water laws, policies, and
management institutions. This task adapts and extends the optimization model developed by Booker for
the Colorado Basin (Booker 1995). Despite similarities, there are several important differences between
the Rio Grande and Colorado basins dealt with in the present study. For example, the Rio Grande Basin
sees more substitution of groundwater for surface water in droughts, and the interstate water allocation
specified by the Rio Grande Compact has no counterpart in the Colorado Basin. Moreover the Rio
Grande has a much longer history of settlement and related agricultural water use than the Colorado,
with the history of irrigation exceeding 400 years in the Las Cruces, New Mexico area alone.
Hydrologic ModelThe hydrology component of the overall model accounts for sources and uses of water from the
San Luis Valley, Colorado to the El Paso, Texas area. This work was supervised by Dr. Phil King and
Dr. Raghavan Srinivisan, with cooperation from Dr. Seiichi Miyamoto. The hydrologic model
component was based on existing local hydrologic models and data. These include models developed by
the U.S. Bureau of Reclamation, local irrigation districts, municipalities, the International Boundary and
Water Commission, and the U.S. Geological Survey. The Soil and Water Assessment Tool (SWAT)
developed by hydrologists at Texas A&M University is a basin-scale hydrologic/water quality model
11
(Arnold et al. 1993) developed by the U.S. Department of Agriculture-Agricultural Research Service
and Texas Agricultural Experiment Station-Blackland Research Center. The SWAT model has been an
important source of hydrologic data.
Many hydrology models are quite specialized and detailed. By contrast, this study focuses on the
larger scale of the Rio Grande system, for which major sources and uses of water are accounted.
Hydrologic performance characteristics relevant to this study were derived from existing work.
Characteristics of the river system, such as reservoir capacities, stage-discharge and stage-surface area
relationships, river conveyance and storage capacities, conveyance times, gains/losses, and diversions
and return flows over seasonal time intervals has been derived in a simplified form from smaller scale
more detailed models. Modeling system behavior at this level facilitated links to an economic damages
model and to an institutional response model.
Modeling ConsultantDr. James Booker, who completed a similar integrated hydrologic, economic, and legal drought
management model in 1994 for the Colorado River Basin, originally worked as a consultant with Mr.
Tom Lynch to build the model for the Rio Grande. In January 1999, after Mr. Lynch developed a
prototype model and graduated from New Mexico State University, Dr. Booker completed the model.
This model development work has consisted of several stages.
First, a strategic planning process was used to define the model design and components needed
to achieve study objectives. A critical task was to identity the basic network structure, and appropriate
spatial and temporal scales. Secondary areas included a conceptual design for linking groundwater use to
surface flows, and implementing existing and prospective reservoir operations. The model treatment of
native flows, withdrawals, consumptive use, and return flows will also be defined at this stage. The data
structures designed for the Rio Grande modeling framework needed to be accessible to and supportive of
other project needs while being easily applied within the GAMS (General Algebraic Modeling System)
12
environment. GAMS is a mathematical optimization software package whose code is readable both by
people and computers. Its readability by people was expected to be an advantage in peer review of the
model, and its application to proposed water management plans.
Second, a prototype model that incorporates the model features defined at the strategic planning
stage was developed. It has served two purposes. It served to validate initial design concepts and to
identify at an early stage areas where design changes were necessary. It also provided early feedback to
the full project team, serving as a vehicle to improve communication across disciplines and focus efforts
on the critical areas needed to achieve overall objectives.
Third, implementing the completed Basin model to address institutions for adapting to drought
required interaction among a number of project researchers. Possible water management scenarios were
suggested based on preliminary results, and promising alternatives needed to be implemented. Defining
such institutions within the model framework was not straightforward and was best accomplished with
significant interaction among project researchers.
Finally, an important product of this project is an integrated modeling framework for the Rio
Grande Basin that will be useful for water management and institutional analysis.
Algorithm for Defining Water Use Patterns in DroughtNumerous water laws, court decisions, water rights patterns, and historical water use patterns as
well as reservoir operating procedures in Colorado, New Mexico, and Texas, dictate the distribution of
Rio Grande Basin water, both in normal and drought periods. Under the supervision of Dr. Charles
DuMars the research group developed an algorithm incorporating the allocation of flows among all such
parties. This algorithm will illustrate the allocation of flows during average years, when the river’s flows
fulfill all claims as well as during low-flow years when the river’s waters are insufficient to meet all
demands. The Rio Grande Compact is the major institution governing the allocation of these
streamflows.
13
The current institutional and system operating response to drought-induced shortages was coded
as a series of mathematical formulas, written in the GAMS language. The formulas were consistent with
the response of the current operating systems to drought under current water management institutions.
These formulas accounted for the water use priorities within each of the three Basin states. That is, the
change in pattern of water diversions that occur during drought periods compared to normal periods are
largely a function of the dates of priority and extent of use permitted to the various water right owners.
Drought-induced changes in water use patterns also depend on what kind of water right is defined (e.g.,
diversion versus storage rights), location of the water right and water right owner, and extent of the right.
Task 3: Develop an Economics Drought Damage Component
This work component has analyzed the economic damages associated with selected drought
scenarios by identifying the magnitude, location, and distribution of economic drought damages under
present reservoir operating rules, policies, and management institutions.
Economic Impacts and ResponsesA large body of theoretical and empirical literature has been developed that focuses on
appropriate approaches for measuring direct economic impact of changes in water use levels (Young and
Gray 1972; Gray and Young 1983; Gibbons 1986).
Estimating net willingness to pay for increments of water supply or for institutional adjustments
that alter those increments of water supply is the accepted approach developed over many years in the
14
economics scientific literature. Other monetary-based approaches include measures of value added, that
is, income to primary regional resources (Young and Gray 1985), and gross revenue or sales per unit of
water.
Three approaches for measuring net willingness to pay are available. The first approach employs
statistical analysis of water use decisions by users. This approach is used primarily in the household and
recreational sectors (Young 1973; Howe 1983; Daubert and Young 1981; Martin et al. 1984).
The second approach, change in net income, imputes residual changes in net business income to
changes in water use. This approach is used primarily in evaluating agricultural and industrial water uses
(Young and Gray 1972; Kelso et al. 1973).
The third approach, alternative cost, values water in terms of resource savings achieved by water
intensive, rather than existing, production techniques.
Drought Damage Assessment by Category of UseAgriculture
Direct economic damage to commercial agriculture resulting from drought is measured as the
associated loss in net farm income. Income losses were estimated based on drought damage responses to
water supply shortages for each of the major irrigated cropping regions in the basin. Major regions
include the San Luis Valley in Colorado, the Middle Rio Grande Conservancy District near Socorro,
New Mexico, Elephant Butte Irrigation District near Las Cruces, New Mexico, and the El Paso Water
Conservation District #1 near El Paso, Texas.
Drought damage estimates for agriculture were based on crop-water yields, crop prices, and costs
of agricultural production, including water delivery cost differentials between surface water and
groundwater. The economic value of water in irrigation depends on opportunities for conservation,
substitution, or reduced use of water in the face of increasing water scarcity (e.g., McGuckin et al. 1992).
15
Agronomic crop water yield response data are already available for many parts of the basin, and
have been used to the extent possible. For crop prices and costs of production, data in crop enterprise
budgets published by the Colorado, New Mexico, and Texas Agricultural Experiment Stations, the
Bureau of Reclamation, and the individual irrigation districts were used. Examples include Lansford
(1995) and Libbin (1995).
We conducted original research for all the important agricultural areas of the basin described
above, in which linear programming models were used to replicate observed current and historical
cropping patterns under various water supply conditions. For these models, agronomic yield response
functions to water shortages were assembled in order to estimate impacts of water supply reductions on
farm incomes. Equivalent methods are described in Booker and Colby (1995) and Booker and Young
(1994).
Similar linear programming models have seen extensive previous development and use under the
direction of Dr. Robert Young (e.g., Taylor and Young 1995) and Dr. Ron Lacewell (e.g., Bryant, et al.
1993). Dr. Robert Young and Dr. Marshall Frasier focused on agricultural areas in San Luis Valley,
Colorado and in the Middle Rio Grande Conservancy District in New Mexico. A Ph.D. dissertation was
completed by Mark Sperow at Colorado State University (1998), under supervision of Dr. Frasier, that
examined agricultural sector response to drought in the San Luis Valley, Colorado. Dr. Ron Lacewell and
Dr. John Ellis developed agricultural drought damages for the Middle Rio Grande Conservancy District
and the Elephant Butte Irrigation District in New Mexico, and the El Paso Water Improvement District
#1 in El Paso, Texas.
Municipal and Industrial (M&I)The economic value of water used to meet M&I demands is based on water prices charged to
customers, water use per household, and total numbers of households served. Albuquerque, Las Cruces,
and El Paso are all large cities whose water use is connected to the Rio Grande. All are expected to
experience considerable population growth in the years ahead, and their demand for water will likely
16
increase. Dr. Tom McGuckin supervised the estimation of drought impacts for M&I uses, with assistance
from Ms. Donna Stumpf.
Demand for water per household depends on average and incremental price per gallon, weather,
income, size structure of household, and numerous demographic factors. Water use rates and the factors
that influence those use rates, vary considerably by city, year, and seasons within a year. The total
demand for water is demand per household times number of households. Data on population forecasts for
these cities an important part of this study, have been obtained from census sources where possible.
Drought damage estimates for M&I water were developed from secondary sources. Numerous
studies have been published on the economic value of water for M&I uses, some of which had
application to the Rio Grande Basin. A small sample of these studies include Griffin and Chang (1991),
Foster and Beattie (1979), Griffin (1990), Jones and Morris (1984), Opaluch (1982), Martin et al. (1984),
Nieswiadomy (1992), and McKean et al. (1996), Taylor and Young (1995). Residential price elasticities
of demand for water have also been estimated using contingent valuation methods (Thomas and Syme
1988).
Dr. McGuckin has developed data on residential water demand for Albuquerque and Las Cruces
as well as El Paso from several previous studies, based on water use from 1980-1995. Household
income, temperature, precipitation, number of service connections, and utility rate schedules have been
included within a regression equation to estimate the effects that each have on historical residential water
use. He has also explored the extent to which the presence of various non-price conservation programs
(e.g., public information campaigns, odd-even watering schedules, low-flow toilet rebates)
accompanying various rate schedules influences residential water use.
17
Hydroelectric Power Streamflows, mostly from reservoir storage, produce hydroelectric power at a number of Basin
dams, including El Vado, Abiquiu, and Elephant Butte reservoirs. Hydroelectric values of water are
based on utility costs avoided by not having to supply power demands from alternative sources, such as
thermal.
In the Rio Grande Basin, hydropower production occurs both during peak and base load periods,
displacing base load (primarily coal) facilities and peak load (primarily gas turbine and oil) facilities.
The cost of peaking power production is typically significantly greater than for base load production, so
hydropower facilities could be operated to increase total production during peak demand periods, which
is typically summertime in this region. However, competing demands for water in the Rio Grande Basin
are considerable, so hydro production typically is not timed to occur during peak power demand periods.
Hydroelectric economic values of water were obtained where possible from regional and local
utilities. For example, the Public Service Company of New Mexico supplies power for much of central
New Mexico, while the El Paso Electric Company supplies power to southern New Mexico and west
Texas.
RecreationWater-based recreation is an important part of leisure activities of many residents of and visitors
to the Rio Grande Basin, and water-related recreation opportunities contribute to tourism and related
economic activities in much of the southwestern U.S.
Instream and reservoir-based recreation attract considerable numbers of visitors and both are
affected negatively in a drought. Policy makers can make more informed decisions about stream and
reservoir management if they know the economic benefits provided by streamflows and reservoir levels
for recreation activities, such as fishing, boating, rafting, swimming, and sightseeing. Several studies
have shown that recreational values of Basin reservoirs and streams are a declining function of reservoir
contents and streamflows, respectively. Considerable work on recreation economic values of water has
18
also been published by Daubert and Young (1981), Johnson and Walsh (1987), Sanders and others
(1990), Ward (1987), Ward (1989), and Cole and Ward (1994). More recently, estimated recreational
values of water have been observed in the range of $6 to $600 per acre-foot, depending on reservoir
contents and other characteristics of the reservoir at which the recreation occurs (Ward et al. 1996).
Recent work has estimated recreational economic values of water in Lake Travis, Texas to be
between $109 and $135 per acre-foot (Lansford and Jones 1995). Recreational economic values of water
for coastal sites have also been estimated for Texas (Ozuna and Gomez 1994; Ozuna, et al. 1993). The
present study has drawn from these and other sources of literature to develop estimates of recreation
economic drought damages.
Task 4: Identify Institutional Adjustments to Drought
This study component identified how current water management institutions could be modified
to alter the basin’s current response to drought. It complements Task 3, which identifies only how
current institutions affect the basin’s response to shortage.
This study component aimed to predict how water use patterns of the Rio Grande Basin selected
drought shortage scenarios would be altered by modified water management laws and institutions. It also
predicted how economic damages would be altered by such institutional changes. The goal was to find
institutional responses that would reduce the region’s vulnerability to severe drought by reducing overall
economic damages. A recently published study of sustained and severe drought in the Colorado River
Basin identified several potential institutional responses to drought in that area (Booker 1995). Several of
these responses had direct application to the present Rio Grande Basin analysis.
Professor Charles DuMars has studied most important institutions constituting the law of the
river. The most important institution in this region is the Rio Grande Compact, with somewhat less
emphasis on the Mexican Water Treaties of 1906 and 1944, federal reclamation law, the Pueblo Water
19
Rights Doctrine, and major environmental laws, including the Endangered Species Act and the Clean
Water Act. His analysis included a brief summary of the state water law for each of the three Basin
states.
DuMars has explained how each of the laws and institutions would function under different
drought scenarios. To the degree these institutions stand as barriers to water transfer and use, these laws
will be considered as constraints that must either be honored or altered through the political process.
The analysis began with an investigation of all of the above institutions through a literature
search. After this research was completed, work focused on a matrix that illustrates the laws, their
hierarchy, their potential impacts under different drought circumstances, and the degree of flexibility
within each law to adjust to water scarcity.
After compiling the relevant laws, the agencies responsible for enforcing these laws were
contacted in order to verify the actual application of the laws to the facts. As the data were developed,
Professor DuMars worked closely with other team members to monitor their progress and indicate where
and how the legal institutional principles compared with the factual information. This factual information
was integrated into the overall report results as needed both as an individual chapter and as explanatory
information needed to address fully related issues.
Because it is difficult to foretell what institutional changes will result from severe drought, the
hydrology model component was designed to be flexible enough to represent the spectrum of possible
operation rules. The model accommodates a large number of operating and allocation rules as well as
overall systems of allocation.
Task 5. Hydrologic-Economic-Legal Policy Analysis
This task investigated the economic implications of alternative institutional arrangements for
allocating Rio Grande Basin waters in times of shortage. The model was formulated as a mathematical
20
program and solved for a variety of scenarios, including the 44-year period covering the 1950s drought,
1942-1985, and a 44-year period in which inflows were equal to average inflows defined for the period
of record. In addition 50 and 100-year drought scenarios were developed, but time constraints prohibited
complete integration of those scenarios into the final model.
Economic damages attributable to a severe drought for each region and sector were estimated by
comparing the baseline long-run average flow results with the results for the 1950s drought scenario
replicated for the next 44 years. Manipulations of the model permits analyses of institutional
adjustments, such as carryover storage, increased irrigation efficiency, building new reservoirs, and
water market development.
Numerous current institutional constraints set limits on how the river or its reservoirs can be
operated. Three of the more important include the Rio Grande Compact, federal reservoir authorization,
and contracts signed by various water users.
Potential institutional responses to drought include those that affect river management, changes
to legal environments, and market-based responses such as water banks. A few examples below were
originally considered, but modified as described in more detail subsequently in the results.
River Management� Evaporation losses can be reduced by reallocating storage to high elevation reservoirs
� Reservoir operating rules might be evaluated to alter the balance between hydropower and
different uses
Changes to Legal Environment� Sale or lease of rental of water conserved due to investments made for water conservation; this is
not currently permitted under New Mexico, Colorado, or Texas water law
� Proportional sharing of shortfalls; for rivers adjudicated in Colorado and New Mexico, the
current seniority system of water rights produces an uneven pattern of sharing shortfalls
21
Market Based Operations� Intrastate water banks: within a given state, institutions might be set up to reallocate that state’s
total drought-induced shortfall, using state water banks, or direct water marketing among users;
interstate compacts such as The Rio Grande Compact would still be used to allocate shortfalls
among states
� Interstate water banks: water banking or water marketing across state lines would be examined;
if this occurred, the added benefits from water marketing may occur if state level transfers do not
bring about similarly-valued water uses across states; implementing interstate water banks would
need to account for the Compact through such measures as credits.
� Optioning contracts for temporary use of irrigation water (Young and Michelsen 1993); contracts
for temporary use of irrigation water rights may be a low cost arrangement for providing drought
insurance for urban areas, such as Albuquerque or El Paso
Drought Scenarios for the Rio Grande Basin
A major aim of this study was to develop scenarios for the 50-year and 100-year droughts in the
Rio Grande Basin at the Rio Grande’s headwaters in Colorado and New Mexico in addition to replicating
the extended and severe drought of the 1950s. The following steps were taken to achieve this goal:
1) Identify the unimpaired gaging points in Rio Grande Basin, termed headwater flows, at which
streamflow is essentially unaltered by human activities.
2) Statistically analyze drought durations and severity at the unimpaired gaging points.
3) Calculate monthly disaggregation coefficients for the annual streamflow series at the unimpaired
gaging points, which characterize the monthly allocation of these annual flows.
4) Characterize 50-year and 100-year drought scenarios for those unimpaired gaging points.
The analysis described below was based on historical streamflow data from USGS gaging
1For example ungaged inflows originating in northern New Mexico are calculated based on their correlationwith historic Rio Grande flows measured at the Del Norte gage. Central New Mexico arroyo flows are estimated basedon correlations with the Rio Salado. For the 50 and 100 year drought scenarios, these inflows represent flows associatedwith the kind of drought expected to occur once in 50 years or once in 100 years respectively.
22
stations in the basin. These stations capture the majority of unimpaired inflows to the basin, and include
both snowpack runoff and rainfall runoff dominated sub-basins. Additional basin inflows, ungaged
flows, are characterized through correlations with the set of representative inflows. 1
Selection of Unimpaired Gaging Points in Rio Grande BasinIn order to model the 50-year and 100-year droughts in the Rio Grande Basin, it was necessary to
analyze the behavior of the system in terms of natural streamflow patterns. These natural streamflows
could then be routed through the system, and management decisions could be made concerning reservoir
releases and streamflow diversions. For this study, as shown in Figure 1-1 one gage was chosen on the
following rivers as being representative of unimpaired streamflow in the river basin.
1) Rio Grande near Del Norte, CO
2) Conejos River Index Flows: (a) Conejos River at Mogote, CO plus (b) San Antonio
River at Ortiz, CO plus (c) Los Pinos River near Ortiz, CO
3) Rio Chama near Chamita, NM
4) Jemez River below Jemez Canyon Dam, NM
5) Rio Puerco near Bernardo, NM
6) Rio Salado near San Acacia, NM
Each of these gages was chosen based on the criterion that no major management decisions
upstream of the gage alters streamflow at that gage. Such management decisions might include reservoir
operations, by which an increase in storage over a time period would decrease flow at the downstream
gage or vice versa; a streamflow diversion to agricultural, municipal, or industrial water users, which
23
would decrease the streamflow at the downstream gage; or a discharge into the river from water users,
which would increase the streamflow at the gaging point.
For the Rio Grande, the gaging point near Del Norte, Colorado, was chosen to represent natural
flow. Although this point is below the Rio Grande Reservoir, this reservoir was considered to have
insignificant storage capacity relative to the monthly streamflow of the Rio Grande. Thus, impacts to the
monthly streamflow due to changes in storage in the reservoir were considered negligible. This gaging
point is also useful because it is the point on the Rio Grande on which Colorado’s compact delivery
requirement to New Mexico is based. Thus, the record of streamflow at this gage is long and consistent.
For the Rio Conejos, the gaging point near Mogote, Colorado, was chosen as representative of
natural flow. This point is below Platoro Reservoir on the river, but again the effects of changes in
reservoir storage were considered negligible due to the reservoir’s small storage capacity. Colorado’s
compact delivery requirement to New Mexico from the Rio Conejos is determined by the flow at this
gaging point plus flow of the San Antonio and Los Pinos rivers.
The unimpaired flow in the Rio Chama was modeled based on the flow at the gaging point near
Chamita, New Mexico, after subtracting the flow in Willow Creek near Azotea Tunnel. This net Willow
Creek flow represents the contribution to the Rio Grande Basin from the San Juan-Chama interbasin
diversion project, which is considered a management decision.
Natural streamflow on the Rio Jemez was modeled according to the flow at the gaging point near
Jemez, New Mexico. This gaging point is above the Jemez Canyon Reservoir and is considered
representative of unimpaired flow in the river.
24
For the Rio Puerco and Rio Salado, the gaging points at their intersections with the Rio Grande
were chosen to represent unimpaired flow. These gaging points are near Bernardo, New Mexico, and
near San Acacia, New Mexico, respectively, and were selected because there are no reservoirs, diversion
points, or discharge points above these gages.
Statistical Analysis of Drought Duration and Severity at Unimpaired Gaging PointsBased on the unimpaired streamflow points chosen for the Rio Grande and its tributaries, the
next step was to determine the probabilistic distributions for the duration and severity of droughts at each
of these points. To perform such an analysis, based on a limited record of annual streamflows at the
gaging points, a Monte Carlo technique was employed. This involved the following four steps:
1) Determine the best-fitting frequency distributions for the annual streamflow time series
at each of the six unimpaired gaging points and the parameters thereof.
2) Generate 10,000 years of synthetic streamflow data that use the best statistical
distributions that are fit to actual historical flows.
3) Determine the best-fitting frequency distributions for drought duration.
4) Estimate the relationship between drought severity and drought duration at each
unimpaired gaging point.
With these steps completed, the statistical characteristics of drought duration and the relationship
of drought severity to drought duration is known for each of the unimpaired gaging points. This means
the statistical behavior of droughts in terms of annual streamflow is known for each gaging point.
Frequency Distributions for Streamflow at Unimpaired Gaging PointsProbability distributions of drought parameters were identified by analyzing annual streamflow
series at the unimpaired gaging points for the same. To do this, several candidate probability
distributions were considered for each gaging point, each of which had an excellent potential of fitting
2In this section of the report dealing with developing drought scenarios for the Rio Grande Basin, streamflowis typically measured in the USGS format of cubic feet per second over a one-year period (cfs-years), except whereotherwise noted. To translate cfs-years into acre-feet per year, multiply by 1.9837, a number slightly less than 2. Forexample, 20,000 cfs-years equals 20,000 times 1.9837 or 39,674 acre-feet per year.
25
Figure 3-1Rio Chama Annual Streamflow Probability Distributions
0
0.000001
0.000002
0.000003
0.000004
0.000005
0.000006
0 100000 200000 300000 400000 500000 600000
Annual Flow (cfs-years)
px(
x)
Lognormal Distribution
Gamma Distribution
Weibull Distribution
the streamflow data. The distribution that best fit the original data was chosen to characterize the annual
streamflow series at each point. The Gamma, Lognormal, and Extreme Value Type III Minimum
(Weibull) were considered excellent candidates, because all have shapes that adapt to a wide range of
annual streamflow water production. Figure 3-1 shows that each of these distributions has two added
characteristics desirable for representing annual streamflow series: 2
1) The distributions are bounded on their lower ends at zero.
2) The distributions allow for skewness about the mean.
These two properties reflect the physical behavior of annual streamflow series. The first property
is required because no streamflow series will have negative values. The second characteristic allows for
the likelihood of either extremely high flows or extremely low flows, which fits well with the flashy
26
Figure 3-2Rio Salado Annual Streamflow
0
5000
10000
15000
20000
25000
30000
35000
1945 1950 1955 1960 1965 1970 1975 1980 1985
Year
An
nu
al S
trea
mfl
ow
(cf
s-yr
s)
nature of western rivers like those in the Rio Grande Basin. Figure 3-2 illustrates the characteristics of
streamflows for the Rio Salado. While in 1958, 1978, and 1979, annual streamflow was almost zero,
annual streamflow in 1972 was close to 33,000 cfs-years. This is more than six times the average annual
streamflow for the Rio Salado. Clearly, the probability distribution used to model this series must allow
extremely high or low flows to have a good chance of occurrence.
The determination of the frequency distributions for the annual streamflow time series at each
unimpaired gaging station in the Rio Grande Basin required the following steps:
1) For each river’s annual streamflow series, estimate the distribution parameters for each
of the candidate distributions.
2) Perform a Kolmogorov-Smirnov goodness of fit test to determine which of the candidate
distributions best fits each annual streamflow series.
Calculation of Distribution Parameters This section describes methods used to fit the gamma, lognormal, and Weibull distributions to
27
the annual streamflow series for each stream reach. Each mathematical density function measures the
probability that a given annual streamflow will occur, and is estimated based on analysis of past
streamflow records.
The parameters for the gamma and lognormal distributions were calculated using the Microsoft
Excel spreadsheet package (Microsoft 1996) and standard estimation techniques (Haan 1977). The
parameters for the Weibull distribution were estimated using the SOLVER routine in the Excel
spreadsheet, again using standard techniques. These calculations are described below.
Gamma Distribution. The gamma density (Haan 1977) function for a river’s annual streamflow is given
by:
px (x) = �0 x0-1 e -8x / �(�) x, �, � > 0 (3.1)
where x is annual streamflow in cfs-years, � and � are gamma distribution parameters that are estimated
based on records of actual measured historical streamflow, as this streamflow varies from one year to the
next. The expression �(�) is the gamma function, which cannot be written in a simple form. However, its
following properties can be used to compute it with any precision desired.
�(�) = (� - 1)! for � = 1, 2, 3, �
�(� + 1) = ��(�) for � > 0 (3.2)
�(1) = �(2) = 1
�(½) = (�) ½
Table 3-1 below shows values of �(�) for a range of � in which 1.0 � � � 2.0. For other values of the
parameter �, the equations above can be used.
28
Table 3-1. Gamma Function Values for a River’s Annual Streamflow in cfs-years� gamma(�) � gamma(�) � gamma(�) � gamma(�)
1.01 0.99433 1.26 0.90440 1.51 0.88659 1.76 0.921371.02 0.98884 1.27 0.90250 1.52 0.88704 1.77 0.923761.03 0.98355 1.28 0.90072 1.53 0.88757 1.78 0.926231.04 0.97844 1.29 0.89904 1.54 0.88818 1.79 0.928771.05 0.97350 1.30 0.89747 1.55 0.88887 1.80 0.931381.06 0.96874 1.31 0.89600 1.56 0.88964 1.81 0.934081.07 0.96415 1.32 0.89464 1.57 0.89049 1.82 0.936851.08 0.95973 1.33 0.89338 1.58 0.89142 1.83 0.939691.09 0.95546 1.34 0.89222 1.59 0.89243 1.84 0.942611.10 0.95135 1.35 0.89115 1.60 0.89352 1.85 0.945611.11 0.94739 1.36 0.89018 1.61 0.89468 1.86 0.948691.12 0.94359 1.37 0.88931 1.62 0.89592 1.87 0.951841.13 0.93993 1.38 0.88854 1.63 0.89724 1.88 0.955071.14 0.93642 1.39 0.88785 1.64 0.89864 1.89 0.958381.15 0.93304 1.40 0.88726 1.65 0.90012 1.90 0.961771.16 0.92980 1.41 0.88676 1.66 0.90167 1.91 0.965231.17 0.92670 1.42 0.88636 1.67 0.90330 1.92 0.968781.18 0.92373 1.43 0.88604 1.68 0.90500 1.93 0.972401.19 0.92088 1.44 0.88580 1.69 0.90678 1.94 0.976101.20 0.91817 1.45 0.88565 1.70 0.90864 1.95 0.979881.21 0.91558 1.46 0.88560 1.71 0.91057 1.96 0.983741.22 0.91311 1.47 0.88563 1.72 0.91258 1.97 0.987681.23 0.91075 1.48 0.88575 1.73 0.91466 1.98 0.991711.24 0.90852 1.49 0.88595 1.74 0.91683 1.99 0.995811.25 0.90640 1.50 0.88623 1.75 0.91906 2.00 1.00000
Separate parameters, � and �, were estimated using the relevant annual streamflow time series
for each of the six headwater flows. It is a two-stage method, based on the method of maximum
likelihood regression.
For the first stage the following calculations are made:
y = ln(avg(x)) - avg(ln(x))
� est = [ 1 + (1 + 1.333y) ½ ] / 4y (3.3)
� est = �est / avg(x),
where x is total annual streamflow in cfs-years.
For the second stage these values of � and � were adjusted to gain greater precision using the
29
following method:
E(�est - �) = 3�est / n
� cor = �est - E(�est - �) (3.4)
� cor = �cor / avg(x)
Demonstrating this method using the example of the time series on Rio Chama flows at Chamita,
the calculations performed to calculate the gamma parameters are shown below:
Table 3-1a. Gamma Parameter Calculation,
Rio Chama
Stage 1
avg (x) = 176,785 = average annual flow (cfs-years)
avg (ln x) = 11.96 (3.4a)
ln (avg x) = 12.08
y = 0.11794
� = 4.40
� = 2.49E-05
Stage 2
E(� est-� ) = 3 �est / n = 0.22001
� cor = 4.18 (3.4b)
� cor = 2.36E-05
�(� ) = 7.56
The gamma distribution parameters and the derived gamma distributions were estimated for each
of the six headwater gages for the Rio Grande Basin.
Lognormal Distribution. The lognormal density function for annual streamflows is as follows:
30
pX(x) = (2�x2 �y2) -1/2 exp[-½(lnx - µy)
2/�y2] x > 0 (Haan 1977) (3.5)
where x is annual streamflow, in cfs-years, and y = ln(x) is the natural logarithm of annual streamflow;
µy and �y2 are the mean and variance of y, respectively. Table 3-2 illustrates the estimation of the
lognormal distribution parameters for annual streamflows on the Rio Conejos:
Table 3-2. Estimated Parameters for Distribution of Rio Conejos Streamflows at Mogote gage,measured in cfs-years, Lognormal Distribution
Year Streamflow= x
ln(Flow) =y
Year Streamflow= x
ln(Flow) =y
Year Streamflow= x
ln(Flow)=y
1913 78,557 11.27 1940 77,283 11.26 1967 114,350 11.651914 125,127 11.74 1941 194,437 12.18 1968 117,866 11.681915 124,594 11.73 1942 142,769 11.87 1969 134,216 11.811916 174,988 12.07 1943 98,732 11.50 1970 121,021 11.701917 175,507 12.08 1944 148,433 11.91 1971 89,127 11.401918 112,676 11.63 1945 121,064 11.70 1972 61,029 11.021919 123,450 11.72 1946 72,420 11.19 1973 150,296 11.921920 216,689 12.29 1947 110,601 11.61 1974 81,953 11.311921 132,206 11.79 1948 145,624 11.89 1975 137,835 11.831922 154,323 11.95 1949 144,744 11.88 1976 110,041 11.611923 179,737 12.10 1950 85,563 11.36 1977 39,720 10.591924 152,678 11.94 1951 61,864 11.03 1978 91,304 11.421925 112,015 11.63 1952 186,842 12.14 1979 153,749 11.941926 131,657 11.79 1953 82,342 11.32 1980 147,169 11.901927 164,706 12.01 1954 68,183 11.13 1981 60,819 11.021928 105,584 11.57 1955 68,320 11.13 1982 158,120 11.971929 167,354 12.03 1956 84,909 11.35 1983 139,530 11.851930 107,958 11.59 1957 164,175 12.01 1984 124,222 11.731931 68,870 11.14 1958 126,576 11.75 1985 185,778 12.131932 186,221 12.13 1959 75,946 11.24 1986 170,622 12.051933 107,615 11.59 1960 105,000 11.56 1987 140,781 11.851934 55,393 10.92 1961 101,639 11.53 1988 82,305 11.321935 148,946 11.91 1962 128,721 11.77 1989 92,785 11.441936 111,980 11.63 1963 66,865 11.11 1990 78,569 11.271937 161,768 11.99 1964 78,397 11.27 1991 124,223 11.731938 158,456 11.97 1965 154,028 11.94 1992 89,531 11.401939 86,728 11.37 1966 120,465 11.70 1993 138,280 11.84
µy = 11.65 �y2 = 0.12
The lognormal distribution parameters were estimated for each of the six headwater gages using
the methods described.
31
Weibull Distribution. The Weibull density function for a river’s annual streamflows is given by:
pX(x) = � x"-1 �-" exp [- (x/�) " ] x � 0; �, � > 0 (Haan 1977) (3.6)
where x is annual streamflow for the given stream, measured in cfs-years, and � and � are Weibull
distribution parameters. Its mean and variance are:
E(x) = � �(1 + 1/�) (3.7)
Var(x) = �2 [ �(1 + 2/�) - �2 (1 + 1/�)]
The parameters, � and �, were estimated for each of the six headwater gages using observed
historical annual streamflow. This method requires substituting the sample mean and variance for the
unknown population mean and variance, respectively, and then solving both equations simultaneously to
obtain an estimate of � and �. This solution was obtained using the SOLVER routine in Microsoft Excel.
Table 3-3 illustrates estimation of the Weibull parameters, using the example of annual streamflow series
for the Rio Grande at Del Norte.
Table 3-3. Estimation of Weibull Distribution Parameters for Annual RioGrande Headwater Streamflows, Del Norte gage (cfs-yrs)
µ = 331,868 (cfs-yrs) µgen = 268,647 (cfs-yrs) � =4.00 E+09
�2 = 1.21E+10 �2gen = 1.21E+10 � = 2.93E+09
� = 2.6074 SSR = 6.93E+09� = 302,347g1 = 1+1/� = 1.3835263
g2 = 1+2/� = 1.7670527
�(g1) = 0.88854
�(g2) = 0.92137
The SOLVER routine was used to minimize the sum of the squared residuals (SSR) between the
sample and generated mean and the variance of the annual streamflow series by iteratively varying � an
�.
Kolmogorov-Smirnov Goodness of Fit TestThe streamflow distribution with the best fit was chosen for each of the six headwater flow series
32
using the Kolmogorov-Smrinov (K-S) test. This test compares the goodness of fit of a theoretical
mathematical distribution with the distribution of sample streamflows based on the maximum deviation
between the theoretical cumulative distribution function, P x(x), and the sample cumulative density
function, S(x) (Haan 1977). The best fit among the three distributions is defined as the one whose
maximum deviation is smallest. This maximum deviation, D, is defined by: D = max � PX(x) - S(x) �.In order to conclude that a particular probability distribution fits a sample set with a significance
level of ten percent, D must be less than the critical maximum deviation, D crit, defined as follows:
(3.8)
Dcrit�1.22
n
where n is the sample size of the parameter to which the distribution is being fit.
For the gamma, lognormal, and Weibull distributions, the cumulative probability distribution
functions are defined, respectively, as follows (Haan 1977):
PX(x) = 0�x �0 t0-1e-8t / �(�)dt (gamma) (3.9)
where x is annual streamflow, and � and � are gamma distribution parameters defined previously.
PX(x) = 0�x (2� t2 �y
2)-1/2 exp [-½ (ln t - µy)2/�y
2] (lognormal) (3.10)
where x is annual streamflow, and µy and �y2 are the mean and variance of y, respectively, with y = ln(t).
PX(x) = 1 - exp [ - (x/�)" ] (Weibull) (3.11)
where x is annual streamflow, and � and � are Weibull distribution parameters defined previously.
33
The cumulative probability functions for each of the six stream gages were estimated using the
GAMMADIST, LOGNORMDIST, and WEIBULL functions in Microsoft Excel. These functions derive
the theoretical cumulative density functions for each annual streamflow series using, as input, the
parameters calculated as previously described.
For each gage, the sample cumulative density function was generated using the HISTOGRAM
function in Microsoft Excel. This function creates a histogram of a data set, based on selected class
marks, and also calculates the sample cumulative density for the data set, at each class mark. The
distribution with the lowest D, as defined above, was chosen to represent annual streamflow series at
each gaging point. For each K-S test, the maximum deviation, D, was compared with Dcrit to confirm that
the distribution chosen to represent the annual streamflow series fit the sample series with a significance
level of ten percent or better.
The following pages show calculations involved in the K-S test to find the best fit distribution
using the annual streamflow series of the Rio Puerco. Figure 3-3 shows the Rio Puerco’s historical annual
streamflow series. This is followed by K-S calculations, in Table 3-4, comparing the deviations between
the sample and theoretical cumulative density functions. These steps were repeated for six headwater
gages.
34
Figure 3-3Rio Puerco Annual Flow Histogram
0
1
2
3
4
5
6
7
8
1000
5000
9000
1300
0
1700
0
2100
0
2500
0
2900
0
3300
0
3700
0
4100
0
4500
0
4900
0
5300
0
5700
0
6100
0
Annual Flow Class (cfs-yrs)
Fre
qu
ency
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Frequency Sample Cumulative
35
Table 3-4. Goodness-of-Fit Test to Identify Distribution that Best Characterizes AnnualStreamflow (cfs-years), Rio Puerco
Flowcfs-yrs
Freq. SampleCumul.
GammaCumul.
GammaDeviation
LognormalCumul.
LognormalDeviation
WeibullCumul.
WeibullDeviation
1000 0 0.000 0.007 0.007 0.000 0.000 0.036 0.0363000 1 0.020 0.053 0.033 0.024 0.004 0.127 0.1065000 4 0.102 0.127 0.025 0.102 0.000 0.222 0.1207000 5 0.204 0.213 0.009 0.209 0.005 0.313 0.1099000 4 0.286 0.304 0.018 0.321 0.035 0.398 0.112
11000 7 0.429 0.392 0.037 0.425 0.003 0.475 0.04713000 4 0.510 0.475 0.035 0.516 0.006 0.545 0.03515000 4 0.592 0.551 0.041 0.594 0.002 0.608 0.01617000 5 0.694 0.618 0.076 0.659 0.035 0.663 0.03119000 3 0.755 0.678 0.077 0.713 0.042 0.711 0.04421000 1 0.776 0.729 0.046 0.758 0.018 0.754 0.02223000 1 0.796 0.774 0.022 0.795 0.001 0.790 0.00625000 2 0.837 0.812 0.025 0.826 0.011 0.822 0.01527000 0 0.837 0.844 0.007 0.852 0.015 0.849 0.01329000 0 0.837 0.871 0.034 0.873 0.037 0.873 0.03631000 1 0.857 0.894 0.037 0.891 0.034 0.893 0.03633000 2 0.898 0.913 0.015 0.906 0.009 0.910 0.01235000 0 0.898 0.928 0.030 0.919 0.021 0.925 0.02737000 0 0.898 0.941 0.043 0.930 0.032 0.937 0.03939000 0 0.898 0.952 0.054 0.939 0.041 0.947 0.04941000 2 0.939 0.961 0.022 0.947 0.008 0.956 0.017
43000 1 0.959 0.968 0.009 0.954 0.005 0.963 0.00445000 1 0.980 0.974 0.005 0.960 0.020 0.970 0.01047000 0 0.980 0.979 0.000 0.964 0.015 0.975 0.00549000 0 0.980 0.983 0.003 0.969 0.011 0.979 0.00051000 0 0.980 0.986 0.007 0.972 0.007 0.983 0.00353000 0 0.980 0.989 0.009 0.976 0.004 0.986 0.00655000 0 0.980 0.991 0.011 0.978 0.001 0.988 0.00957000 0 0.980 0.993 0.013 0.981 0.001 0.990 0.01159000 0 0.980 0.994 0.015 0.983 0.003 0.992 0.01261000 0 0.980 0.995 0.016 0.985 0.005 0.993 0.01463000 1 1.000 0.996 0.004 0.986 0.014 0.995 0.005
Max. Deviations 0.077 0.042 0.120Deviation crit = 0.174
The lognormal distribution provides the best fit on the annual flow series for the Rio Puerco, because itsmaximum deviation between predicted and observed cumulative distribution is 0.042, whereas theGamma and Weibull both have larger deviations
36
Synthetic Streamflow for 10,000 YearsWith the probabilistic distributions estimated for the unimpaired gages in the basin, Monte Carlo
analysis is used to generate 10,000 years synthetic streamflow data for each of the six gaging points. At
each gage, the 10,000 years synthetic streamflow have the identical statistical properties as the gage’s
relatively short period of historical observed streamflows. The considerably long series of synthetic
streamflow data provides a much larger sampling period to analyze droughts at each gaging point and a
more extensive view of the behavior of extremely wet or dry years at the gage than the much shorter
observed streamflow data.
The cumulative probability function that is uniformly distributed over the interval of probability
(0 to 1) is the basis for random generation of streamflows from a probability distribution (Haan 1977). If
the cumulative probability function PX(x) for the streamflow, in cfs-years, is defined as:
PX(x) = f(x) (3.12)
then to generate a single random value x from PX(x), the following procedure is used:
1) Select a random number Ru from a uniform distribution on the interval (0,1), in which all
numbers have an equal probability of being selected.
2) Set PX (x) = R u., that is identify the cumulative probability associated with R u.
3) Solve this equation for x, in this case, streamflow.
This procedure has the effect of transforming a cumulative probability, R u, between 0 and 1 to
the streamflow whose probability of being less than that flow equals that probability, R u. This process is
sometimes called obtaining the inverse transform of the streamflow probability distribution and is not
possible for all distributions. The details of data analysis for the three distributions are described below.
Gamma Distribution. For the gamma distribution, the inverse transform cannot be obtained so other
methods must be used (Haan 1977). A gamma random variable with a shape parameter on the interval
(0,1) can be constructed as follows:
37
1) Let Ru1, Ru2, and Ru3 be independent uniform random variables on the interval (0,1).
2) Define S1 = Ru11/0 and S2 = Ru2
1/(1-0) .
3) If S1 + S2 � 1.0, define Z = S1/(S1 + S2) and Y = -Zln(Ru3)/�.
Then Y has a gamma distribution with shape parameter � and scale parameter �. If S1 + S2 > 1.0,
then R u1 and R u2 are rejected, and new values are produced.
Finally, a gamma random variable with any shape parameter, �, can be constructed by adding a
gamma variable with an integer value of � and one with � on (0,1). This is the method that was used for
the study. The random uniform variables, Ru1, Ru2, and Ru3, were generated using the RAND(0,1)
function within the Microsoft Excel spreadsheet, and the parameters were used to calculate the values for
S1, S2, Z, Y0-1, Rexp, Yexp, and Ygamma. The first 40 years of the 10,000 years of generated annual
streamflow data for the Rio Salado near San Acacia, NM, are shown in Table 3-5. It should be noted that,
in this case, � =1.02. Therefore, �-1 is on the interval (0,1).
Table 3-5. Generated Annual Streamflows (cfs yrs), first 40 of 10,000 years, Rio Salado Near San Acacia,NM, Gamma Distribution
Yr Ru1 Ru2 Ru3 S1 S2 S1+S2 Z Y0-1 R exp Yexp Y gamma
(Streamflow)cfs-yrs
1 0.154 0.1188 0.9306 0.0000 0.1129 0.1129 0.0000 0.0 0.2038 8105.1 8105.12 0.484 0.9233 0.5796 0.0000 0.9215 0.9215 0.0000 0.0 0.0084 24364.0 24364.03 0.303 0.1942 0.1973 0.0000 0.1867 0.1867 0.0000 0.0 0.9005 534.0 534.04 0.712 0.1357 0.0569 0.0000 0.1293 0.1293 0.0000 0.1 0.1383 10082.9 10083.05 0.086 0.5053 0.9074 0.0000 0.4971 0.4971 0.0000 0.0 0.7562 1424.0 1424.06 0.017 0.9986 0.4709 0.0000 0.9985 0.9985 0.0000 0.0 0.2906 6297.1 6297.17 0.750 0.0545 0.7147 0.0000 0.0508 0.0508 0.0001 0.2 0.6270 2379.0 2379.28 0.709 0.9069 0.4585 0.0000 0.9048 0.9048 0.0000 0.0 0.8223 996.7 996.79 0.507 0.9129 0.3557 0.0000 0.9109 0.9109 0.0000 0.0 0.6903 1888.9 1888.9
10 0.629 0.4950 0.5657 0.0000 0.4867 0.4867 0.0000 0.0 0.9515 253.5 253.511 0.336 0.3526 0.7784 0.0000 0.3439 0.3439 0.0000 0.0 0.4141 4493.2 4493.212 0.163 0.6559 0.3519 0.0000 0.6493 0.6493 0.0000 0.0 0.7184 1685.6 1685.613 0.099 0.4627 0.6560 0.0000 0.4542 0.4542 0.0000 0.0 0.3651 5134.9 5134.914 0.577 0.5413 0.7588 0.0000 0.5334 0.5334 0.0000 0.0 0.3310 5634.6 5634.615 0.558 0.7972 0.2910 0.0000 0.7929 0.7929 0.0000 0.0 0.9031 519.5 519.516 0.464 0.7831 0.7402 0.0000 0.7785 0.7785 0.0000 0.0 0.1085 11318.3 11318.317 0.307 0.860 0.4343 0.0000 0.8569 0.8569 0.0000 0.0 0.1400 10018.1 10018.1
38
18 0.076 0.758 0.0202 0.0000 0.7534 0.7534 0.0000 0.0 0.7845 1236.7 1236.719 0.619 0.8363 0.7251 0.0000 0.8327 0.8327 0.0000 0.0 0.7515 1455.8 1455.820 0.247 0.8157 0.3838 0.0000 0.8117 0.8117 0.0000 0.0 0.5907 2682.8 2682.821 0.458 0.0076 0.2775 0.0000 0.0067 0.0067 0.0000 0.0 0.0152 21341.1 21341.122 0.311 0.5011 0.7601 0.0000 0.4928 0.4928 0.0000 0.0 0.2536 6991.7 6991.723 0.264 0.6482 0.5521 0.0000 0.6415 0.6415 0.0000 0.0 0.8270 967.7 967.724 0.111 0.3173 0.4521 0.0000 0.3086 0.3086 0.0000 0.0 0.9061 502.2 502.225 0.179 0.6966 0.6257 0.0000 0.6905 0.6905 0.0000 0.0 0.2155 7821.2 7821.226 0.626 0.2787 0.0670 0.0000 0.2703 0.2703 0.0000 0.0 0.8759 675.4 675.427 0.113 0.8982 0.9741 0.0000 0.8958 0.8958 0.0000 0.0 0.3982 4692.3 4692.328 0.338 0.5308 0.0112 0.0000 0.5228 0.5228 0.0000 0.0 0.5723 2843.8 2843.829 0.266 0.3578 0.6874 0.0000 0.3491 0.3491 0.0000 0.0 0.1137 11080.3 11080.330 0.840 0.7766 0.3067 0.0006 0.7718 0.7725 0.0008 4.8 0.2370 7337.6 7342.531 0.983 0.3681 0.8889 0.4823 0.3593 0.8416 0.5731 343.8 0.9401 314.8 658.632 0.986 0.1125 0.0557 0.5544 0.1067 0.6612 0.8386 12341.5 0.2865 6369.8 18711.233 0.057 0.3756 0.2205 0.0000 0.3669 0.3669 0.0000 0.0 0.3579 5236.0 5236.034 0.321 0.2544 0.8413 0.0000 0.2461 0.2461 0.0000 0.0 0.8382 899.6 899.635 0.274 0.6192 0.3466 0.0000 0.6121 0.6121 0.0000 0.0 0.8701 709.2 709.236 0.911 0.3878 0.1417 0.0198 0.3791 0.3989 0.0496 494.3 0.4395 4189.9 4684.237 0.789 0.6473 0.2730 0.0000 0.6406 0.6406 0.0001 0.5 0.8748 681.8 682.338 0.663 0.5689 0.6546 0.0000 0.5613 0.5613 0.0000 0.0 0.8083 1084.4 1084.439 0.770 0.1671 0.5758 0.0000 0.1601 0.1601 0.0001 0.3 0.5027 3504.4 3504.740 0.842 0.2573 0.6489 0.0007 0.2490 0.2497 0.0027 6.0 0.5519 3028.7 3034.7
Lognormal Distribution. The lognormal distribution is another case where an analytical inverse
transform cannot be found (Haan 1977). However, a lognormal random variable, Y, can be generated
according to the following function:
Y = exp (� ln(x) RN + µln(x)) (3.13)
where RN is a random observation from a standard normal density distribution, and x represents the
observed streamflow series, and the mean and variance of the log of the observed historical streamflow
series are µln(x) = 9.44 and �ln(x) = 0.7284 respectively, where flow is measured in cfs-years. For this study
random values of RN were generated using the Random Number Generation function in Microsoft Excel.
The first 40 years of streamflow data generated for the Rio Puerco, for which the Lognormal fits well,
are shown in Table 3-6:
39
Table 3-6. Rio Puerco Generated Annual Streamflow, in cfs-yrs, first 40 of 10,000 years,lognormal distribution, in which µ ln(x) = 9.44 and � ln(x) = 0.7284
Year RN
(random number from standard normal distribution with
mean 0 and variance 1)
Ylognormal
(streamflow, cfs-yrs)
1 0.9227 24,7202 -0.7299 7,4183 0.8891 24,1234 2.5212 79,1995 0.7564 21,9016 0.0528 13,1187 -0.1344 11,4468 1.1503 29,1789 0.0610 13,197
10 0.4435 17,43711 -1.6051 3,92112 1.1050 28,23213 0.2419 15,05614 -0.0423 12,24015 -1.0010 6,08816 1.7823 46,23717 -0.2154 10,79018 -1.2954 4,91319 0.6193 19,81820 -0.0455 12,212
21 0.2244 14,86522 0.2997 15,70223 0.0264 12,86824 2.6145 84,77425 -0.4176 9,31226 0.6106 19,69327 -0.4918 8,82328 1.5141 38,03129 1.0614 27,34830 -0.0260 12,38631 0.4674 17,74232 -0.4836 8,87533 -1.1566 5,43634 -1.0262 5,97835 1.5636 39,42836 -0.7806 7,14937 0.2193 14,80938 -1.0159 6,02339 1.0292 26,71540 0.0589 13,176
40
Weibull Distribution. Of the three distributions used in this study, the Weibull is the only one that has an
analytical inverse transform. The inverse transform for the Weibull distribution is as follows:
x = - � [ln(1-Ru)]1/" (Haan 1977) (3.14)
RU can be generated using the RAND (0,1) function in Microsoft Excel.The result is to assign a
streamflow any value of Ru generated randomly over the cumulative probability interval 0-1.
Comparison of Headwater Flows. The gamma distribution fit best for all headwater gages except the Rio
Puerco. For the Rio Puerco, the lognormal fit best. The Weibull did not fit best for any of the six.
Determination of Frequency Distributions for Drought DurationFrom the 10,000 years of synthetic annual streamflow data, the characteristics of the drought
parameters, severity and duration, at each unimpaired gaging point were then evaluated. The statistical
behavior, relative to annual streamflow, of droughts at each of the unimpaired gaging points would then
be known. From this information, 50-year and 100-year drought scenarios were generated for each of the
gages, as described in detail below.
The large sample set of streamflow data with the same statistical properties as the historical
streamflow data provided a large sample of droughts in the Rio Grande Basin. From this, the drought
events were identified throughout the streamflow series as described below.
Exponential, gamma, lognormal, and Weibull probability distributions were fit to the drought
duration and severity(not streamflow),and goodness of fit tests were then performed to determine the
best fit distributions.
Identification of Drought Events. This section describes principles and procedures underlying runs
theory, as used to characterize the drought events for the 10,000 years of synthetic streamflows for each
of the six unimpaired flow gages. The following steps were taken in this process:
41
1) Assign a known percentage of mean annual streamflow, at each gaging point, to
correspond to a drought, defined as the "critical streamflow." For this investigation,
critical streamflow level was assigned a value of 75% of the long-term annual average
streamflow.
2) Set initial storage deficit at zero. As long as annual streamflow remains at or above the
critical streamflow, the storage deficit remains at zero.
3) If annual streamflow falls below the critical streamflow for a year, add that year’s flow
shortfall to the storage deficit using the equation:
deficit i = deficit i -1 + (streamflow crit - streamflow obs) (3.15)
where deficiti is the storage deficit at the end of the given time step, deficit i-1 is the
storage deficit at the end of the previous time step, streamflow crit is the critical annual
streamflow, and streamflowobs is the observed annual streamflow during the given time
step.
4) Continue to track the storage deficit using the equation above until the deficit returns to
zero. At this point the drought has ended. Note that the storage deficit cannot go below
zero.
The first 40 years of generated annual streamflows, and the associated droughts, at the
unimpaired gaging point on the Rio Grande are shown in Table 3-7.
42
Table 3-7. Analysis of Drought Deficits, based on first 40 years of 10,000 years synthetic streamflow, RioGrande at Del Norte gage, (cfs-years)
Average Annual Flow (cfs-yrs) = 332,50775% Average Annual flow = 249,380
Year Annual Flow
(cfs-yrs)
75% aveannual flow
(cfs-yrs)
Storage Deficit
(cfs-yrs)
Cumulative Deficit
(cfs-yrs)
Drought Deficit
(cfs-yrs)
1 379,571 249,380 0 0 02 258,081 249,380 0 0 03 151,103 249,380 98,278 98,278 98,2784 699,228 249,380 0 0 05 37,261 249,380 212,119 212,119 06 356,816 249,380 104,684 316,804 316,8047 940,750 249,380 0 0 08 161,563 249,380 87,818 87,818 87,8189 451,292 249,380 0 0 010 8,705 249,380 240,675 240,675 011 270,485 249,380 219,571 460,246 460,24612 555,126 249,380 0 0 013 620,381 249,380 0 0 014 1,271,655 249,380 0 0 015 472,702 249,380 0 0 016 103,389 249,380 145,992 145,992 017 201,162 249,380 194,210 340,201 018 396,375 249,380 47,216 387,417 019 208,386 249,380 88,210 475,628 020 227,493 249,380 110,098 585,725 021 222,983 249,380 136,495 722,220 022 57,274 249,380 328,601 1,050,822 1,050,82223 794,463 249,380 0 0 024 889,303 249,380 0 0 025 390,543 249,380 0 0 026 240,460 249,380 8,921 8,921 8,92127 1,038,200 249,380 0 0 028 52,458 249,380 196,922 196,922 029 304,495 249,380 141,808 338,730 030 111,891 249,380 279,298 618,027 031 84,944 249,380 443,735 1,061,762 032 53,859 249,380 639,256 1,701,018 1,701,01833 1,738,162 249,380 0 0 034 40,999 249,380 208,381 208,381 035 31,218 249,380 426,544 634,926 634,92636 1,293,570 249,380 0 0 037 159,168 249,380 90,213 90,213 038 65,366 249,380 274,228 364,441 039 201,204 249,380 322,405 686,845 686,84540 623,854 249,380 0 0 0
43
This forty-year stretch of synthesized flows at the Rio Grande gage resulted in nine droughts,
which have the following characteristics shown in Table 3-8.
Table 3-8. Drought Duration and Deficits, Rio Grandeat Del Norte, CO
Drought Duration (years), x
Drought deficit in yearbefore drought ends
(cfs-yrs)
1 98,2782 316,8041 87,8182 460,2467 1,050,8221 8,9215 1,701,0182 634,9263 686,845
For the Rio Grande at Del Norte, CO,a total of 1297 droughts of varying durations were
identified within the 10,000 years of synthesized streamflow. This table shows that a drought of ‘x’
years’ duration is defined as ‘x’ consecutive years in which the cumulative deficit exceeds zero. Similar
methods were used to synthesize droughts of varying severity and duration for the other headwater
gages.
Estimation of Parameters for Drought Severity and Duration. With the drought events identified, using
the method described above, four distributions were fit to the time series of drought durations. The four
distributions included the exponential as well as the gamma, lognormal, and Weibull distributions. Like
the other three distributions, the exponential distribution is bounded by zero on the low end and adapts to
skewness about the mean. Thus, this distribution was considered a good candidate to describe the
drought duration time series.
44
The single parameter for the exponential distribution, �, was estimated using the Microsoft Excel
spreadsheet package and standard estimation techniques. The exponential density function for drought
duration is given by:
pX(x) = � e-8x x, � > 0 (Haan 1977) (3.16)
where x is the drought duration (not annual streamflow), pX(x) is the frequency in which a drought of
that duration occurs. The exponential parameter � is estimated to minimize the difference between the
actual drought duration and its value predicted by the exponential distribution. The ‘observed’ drought
frequency comes from sampling the 10,000 years of synthetic streamflow. The predicted drought
frequency comes from random sampling from the relevant cumulative distribution. The estimate of � is:
� = 1/avg(x) (3.17)
The parameters for the gamma, lognormal, and Weibull distributions were estimated as
described previously. The estimated distribution parameters for the Rio Grande Del Norte, CO drought
duration series are shown below:
Table 3-8a. Rio Grande at Del Norte, CO Drought Duration Distribution ParametersEXPONENTIAL PARAMETERS:
avg (x) = 5.76 (years drought duration)� = 0.17
GAMMA PARAMETERS:avg (ln x) = 1.10ln (avg x) = 1.75
y = 0.65� = 0.91� = 0.158
Correcting for bias:E (�est-�) = 0.0021
�cor = 0.91�cor = 0.158
LOGNORMAL PARAMETERS avg(ln x) = 1.1
stdev (ln x)= 1.04WEIBULL PARAMETERS
�= 0.73�= 5.78
45
Figure 3-4Drought Duration Histogram, Rio Grande at Del Norte, CO
0
50
100
150
200
250
300
350
400
450
1 7 13 19 25 31 37 43 49 55 61 67 73 79 85 91 97 103
109
115
Drought Duration (years)
Fre
qu
ency
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Frequency Sample Cumulative
A similar estimation of drought duration parameters was peformed for the other 5 headwater
gages. Results are shown in Figure 3-4 and Table 3-9 for the 10,000 years of synthetic streamflow for the
Rio Grande at Del Norte, CO.
46
Table 3-9. Distribution of Drought Durations, 10,000 years of synthetic streamflow, Rio GrandeDel Norte, CO headwater flows with 50 and 100-year drought events indicated in bold font
DroughtDuration
SampleFreq
SampleCum.
ExponentialCum.
GammaCum.
LognormCum.
WeibullCum.
ExponentialDev.
GammaDev.
LognormDev.
WeibullDev.
1 412 0.318 0.159 0.180 0.144 0.242 0.158 0.138 0.174 0.0762 238 0.501 0.293 0.314 0.347 0.369 0.208 0.187 0.154 0.1333 130 0.601 0.406 0.424 0.499 0.461 0.195 0.178 0.102 0.1404 97 0.676 0.501 0.514 0.609 0.534 0.175 0.162 0.067 0.1425 90 0.746 0.580 0.589 0.688 0.593 0.165 0.156 0.057 0.1526 36 0.773 0.647 0.653 0.748 0.642 0.126 0.121 0.026 0.1317 44 0.807 0.703 0.706 0.793 0.684 0.104 0.101 0.014 0.1248 29 0.830 0.751 0.751 0.828 0.719 0.079 0.079 0.002 0.1119 22 0.847 0.790 0.789 0.855 0.749 0.056 0.058 0.009 0.097
10 16 0.859 0.824 0.821 0.877 0.776 0.035 0.038 0.018 0.08311 18 0.873 0.852 0.848 0.895 0.799 0.021 0.025 0.022 0.07412 18 0.887 0.876 0.871 0.909 0.819 0.011 0.016 0.023 0.06813 15 0.898 0.895 0.890 0.921 0.837 0.003 0.008 0.023 0.06214 14 0.909 0.912 0.907 0.931 0.852 0.003 0.002 0.022 0.05715 9 0.916 0.926 0.921 0.940 0.866 0.010 0.005 0.024 0.05016 11 0.924 0.938 0.933 0.947 0.879 0.013 0.008 0.022 0.04617 9 0.931 0.948 0.943 0.953 0.890 0.016 0.011 0.021 0.04218 10 0.939 0.956 0.951 0.958 0.900 0.017 0.012 0.019 0.03919 5 0.943 0.963 0.958 0.963 0.909 0.020 0.016 0.020 0.03420 8 0.949 0.969 0.965 0.966 0.917 0.020 0.016 0.017 0.03321 7 0.955 0.974 0.970 0.970 0.924 0.019 0.015 0.015 0.03122 2 0.956 0.978 0.974 0.973 0.930 0.022 0.018 0.017 0.02623 6 0.961 0.982 0.978 0.975 0.936 0.021 0.018 0.015 0.025
24 5 0.965 0.985 0.981 0.978 0.941 0.020 0.017 0.013 0.02325 4 0.968 0.987 0.984 0.980 0.946 0.019 0.017 0.012 0.02126 2 0.969 0.989 0.987 0.981 0.951 0.020 0.017 0.012 0.01827 2 0.971 0.991 0.989 0.983 0.955 0.020 0.018 0.012 0.01628 3 0.973 0.992 0.990 0.984 0.958 0.019 0.017 0.011 0.01529 4 0.976 0.993 0.992 0.986 0.962 0.017 0.016 0.010 0.01430 2 0.978 0.995 0.993 0.987 0.965 0.017 0.015 0.009 0.01331 0 0.978 0.995 0.994 0.988 0.967 0.018 0.016 0.010 0.01032 1 0.978 0.996 0.995 0.989 0.970 0.018 0.016 0.010 0.00833 0 0.978 0.997 0.996 0.990 0.972 0.018 0.017 0.011 0.00634 0 0.978 0.997 0.996 0.990 0.974 0.019 0.018 0.012 0.00435 2 0.980 0.998 0.997 0.991 0.976 0.018 0.017 0.011 0.00436
(50 yr) 0 0.980 0.998 0.997 0.992 0.978 0.018 0.017 0.012 0.002
37 2 0.981 0.998 0.998 0.992 0.980 0.017 0.016 0.011 0.00238 0 0.981 0.999 0.998 0.993 0.981 0.017 0.017 0.011 0.000
47
39 2 0.983 0.999 0.998 0.993 0.983 0.016 0.015 0.010 0.00040 1 0.984 0.999 0.999 0.994 0.984 0.015 0.015 0.010 0.00041 0 0.984 0.999 0.999 0.994 0.985 0.015 0.015 0.010 0.00142 1 0.985 0.999 0.999 0.995 0.986 0.015 0.014 0.010 0.00243 0 0.985 0.999 0.999 0.995 0.987 0.015 0.015 0.010 0.00344 0 0.985 1.000 0.999 0.995 0.988 0.015 0.015 0.011 0.00345 3 0.987 1.000 0.999 0.996 0.989 0.013 0.012 0.009 0.00246 1 0.988 1.000 0.999 0.996 0.990 0.012 0.012 0.008 0.00247 1 0.988 1.000 1.000 0.996 0.990 0.011 0.011 0.008 0.00248 1 0.989 1.000 1.000 0.996 0.991 0.011 0.010 0.007 0.00249 0 0.989 1.000 1.000 0.996 0.992 0.011 0.010 0.007 0.00250 0 0.989 1.000 1.000 0.997 0.992 0.011 0.011 0.007 0.00351 0 0.989 1.000 1.000 0.997 0.993 0.011 0.011 0.008 0.00452
(100 yr)1 0.990 1.000 1.000 0.997 0.993 0.010 0.010 0.007 0.003
53 1 0.991 1.000 1.000 0.997 0.994 0.009 0.009 0.006 0.00354 0 0.991 1.000 1.000 0.997 0.994 0.009 0.009 0.007 0.00355 0 0.991 1.000 1.000 0.997 0.995 0.009 0.009 0.007 0.00456 1 0.992 1.000 1.000 0.998 0.995 0.008 0.008 0.006 0.00357 0 0.992 1.000 1.000 0.998 0.995 0.008 0.008 0.006 0.00458 0 0.992 1.000 1.000 0.998 0.996 0.008 0.008 0.006 0.00459 0 0.992 1.000 1.000 0.998 0.996 0.008 0.008 0.006 0.00460 0 0.992 1.000 1.000 0.998 0.996 0.008 0.008 0.007 0.00561 0 0.992 1.000 1.000 0.998 0.996 0.008 0.008 0.007 0.00562 0 0.992 1.000 1.000 0.998 0.997 0.008 0.008 0.007 0.00563 0 0.992 1.000 1.000 0.998 0.997 0.008 0.008 0.007 0.00564 2 0.993 1.000 1.000 0.998 0.997 0.007 0.007 0.005 0.00465 1 0.994 1.000 1.000 0.999 0.997 0.006 0.006 0.005 0.00366 0 0.994 1.000 1.000 0.999 0.997 0.006 0.006 0.005 0.00467 1 0.995 1.000 1.000 0.999 0.998 0.005 0.005 0.004 0.003
68 1 0.995 1.000 1.000 0.999 0.998 0.005 0.005 0.003 0.00269 1 0.996 1.000 1.000 0.999 0.998 0.004 0.004 0.003 0.00270 0 0.996 1.000 1.000 0.999 0.998 0.004 0.004 0.003 0.00271 0 0.996 1.000 1.000 0.999 0.998 0.004 0.004 0.003 0.00272 1 0.997 1.000 1.000 0.999 0.998 0.003 0.003 0.002 0.00173 0 0.997 1.000 1.000 0.999 0.998 0.003 0.003 0.002 0.00174 1 0.998 1.000 1.000 0.999 0.998 0.002 0.002 0.001 0.00175 0 0.998 1.000 1.000 0.999 0.999 0.002 0.002 0.001 0.00176 0 0.998 1.000 1.000 0.999 0.999 0.002 0.002 0.001 0.00177 0 0.998 1.000 1.000 0.999 0.999 0.002 0.002 0.001 0.00178 0 0.998 1.000 1.000 0.999 0.999 0.002 0.002 0.001 0.00179 0 0.998 1.000 1.000 0.999 0.999 0.002 0.002 0.002 0.00180 0 0.998 1.000 1.000 0.999 0.999 0.002 0.002 0.002 0.00181 0 0.998 1.000 1.000 0.999 0.999 0.002 0.002 0.002 0.001
48
82 0 0.998 1.000 1.000 0.999 0.999 0.002 0.002 0.002 0.00183 0 0.998 1.000 1.000 0.999 0.999 0.002 0.002 0.002 0.00184 0 0.998 1.000 1.000 0.999 0.999 0.002 0.002 0.002 0.00185 0 0.998 1.000 1.000 0.999 0.999 0.002 0.002 0.002 0.00286 0 0.998 1.000 1.000 0.999 0.999 0.002 0.002 0.002 0.00287 0 0.998 1.000 1.000 0.999 0.999 0.002 0.002 0.002 0.00288 0 0.998 1.000 1.000 0.999 0.999 0.002 0.002 0.002 0.00289 0 0.998 1.000 1.000 0.999 0.999 0.002 0.002 0.002 0.00290 0 0.998 1.000 1.000 0.999 0.999 0.002 0.002 0.002 0.00291 1 0.998 1.000 1.000 1.000 0.999 0.002 0.002 0.001 0.00192 0 0.998 1.000 1.000 1.000 0.999 0.002 0.002 0.001 0.00193 0 0.998 1.000 1.000 1.000 1.000 0.002 0.002 0.001 0.00194 0 0.998 1.000 1.000 1.000 1.000 0.002 0.002 0.001 0.00195 0 0.998 1.000 1.000 1.000 1.000 0.002 0.002 0.001 0.00196 0 0.998 1.000 1.000 1.000 1.000 0.002 0.002 0.001 0.00197 0 0.998 1.000 1.000 1.000 1.000 0.002 0.002 0.001 0.00198 1 0.999 1.000 1.000 1.000 1.000 0.001 0.001 0.000 0.00099 0 0.999 1.000 1.000 1.000 1.000 0.001 0.001 0.000 0.000
100 0 0.999 1.000 1.000 1.000 1.000 0.001 0.001 0.000 0.000101 0 0.999 1.000 1.000 1.000 1.000 0.001 0.001 0.000 0.000102 0 0.999 1.000 1.000 1.000 1.000 0.001 0.001 0.000 0.000103 0 0.999 1.000 1.000 1.000 1.000 0.001 0.001 0.000 0.001104 0 0.999 1.000 1.000 1.000 1.000 0.001 0.001 0.000 0.001105 0 0.999 1.000 1.000 1.000 1.000 0.001 0.001 0.000 0.001106 0 0.999 1.000 1.000 1.000 1.000 0.001 0.001 0.000 0.001107 0 0.999 1.000 1.000 1.000 1.000 0.001 0.001 0.000 0.001108 0 0.999 1.000 1.000 1.000 1.000 0.001 0.001 0.000 0.001109 0 0.999 1.000 1.000 1.000 1.000 0.001 0.001 0.001 0.001110 0 0.999 1.000 1.000 1.000 1.000 0.001 0.001 0.001 0.001111 0 0.999 1.000 1.000 1.000 1.000 0.001 0.001 0.001 0.001
112 0 0.999 1.000 1.000 1.000 1.000 0.001 0.001 0.001 0.001113 0 0.999 1.000 1.000 1.000 1.000 0.001 0.001 0.001 0.001114 0 0.999 1.000 1.000 1.000 1.000 0.001 0.001 0.001 0.001115 1 1.000 1.000 1.000 1.000 1.000 0.000 0.000 0.000 0.000
Deviations @ S(x) = 0.980 (50 year drought) Deviations @ S(x) = 0.985 (67 year drought)
Deviations @ S(x) = 0.990 (100-year drought)
Critical Deviation = 0.034
0.0180.0150.010
0.0170.0140.010
0.0110.0100.007
0.0040.0020.003
The Weibull distribution best fits the drought duration series for the Rio Grande at Del Norte, CO.
49
Table 3-10 below shows the estimated probability distributions for each of four distributions for
drought durations for each of the six Rio Grande Basin headwater gages. As shown on the bottom row,
the Weibull distribution provides the best fit for each of the six gages. The Weibull was therefore used to
generate the drought scenarios for both the 50 and 100-year drought events.
Table 3-10. Estimated Drought Duration Parameters, Four Probability Distributions, SixHeadwater Gages, Rio Grande Basin
Distribution Rio Chamaat Chamita
ConejosRiver atMogote
RioGrande atDel Norte
Jemez Riverbelow JemezCanyon Dam
Rio Puerconear
Bernardo,NM
Rio Saladonear San
Acacia NM
EXPONENTIAL avg(x) 5.7300 5.1662 5.7587 5.0701 4.4208 5.5322
λ 0.1700 0.1936 0.1737 0.1972 0.2262 0.1808GAMMA
Stage 1avg (ln x) 1.1400 1.0724 1.1006 1.0614 0.9832 1.0806ln (avg x) 1.7500 1.6421 1.7507 1.6234 1.4863 1.7106
y 0.6100 0.5697 0.6501 0.5620 0.5032 0.6300η 0.9600 1.0209 0.9100 1.0333 1.1391 0.9351λ 0.1680 0.1976 0.1580 0.2038 0.2577 0.1690
Stage 2,Correcting for
biasΕ(η est − η) 0.0022 0.0022 0.0021 0.0022 0.0022 0.0021
η corr 0.9600 1.0187 0.9079 1.0311 1.1369 0.9330
λ corr 0.1680 0.1972 0.1577 0.2034 0.2572 0.1686
LOGNORMAL avg (ln x) = 1.1400 1.0724 1.1006 1.0614 0.9832 1.0806
stdev (ln x) = 1.0500 0.9984 1.0355 0.9872 0.9348 1.0170WEIBULL
α 0.7900 0.8000 0.7326 0.7634 0.9950 0.5051β 5.6500 5.0920 5.7783 4.5755 5.7717 2.2712
Best Fitof 4 distributions
Weibull Weibull Weibull Weibull Weibull Weibull
50
Goodness of Fit Test to Identify Best Distribution. The Kolmogorov-Smirnov (K-S) test was used to
identify which of the candidate distributions best fit the sample distribution of drought durations at each
of the six unimpaired gaging stations. The candidate distribution with the lowest deviation at the point
where the probability of a longer duration drought, S(x) = 0.985 was selected as the best fit. This
definition of best fit assures that the selected candidate distribution fit the sample data well in the region
of particular interest for 50-year and 100-year drought events. A 50-year event is defined as a drought
with a probability of a longer drought equal to 1/50, which is 0.02. In terms of cumulative probability,
this means S(x) is 0.980. A 100-year drought means S(x) = 0.990. The exponential cumulative density
function, S(x), was generated using the EXPONDIST function in Microsoft Excel.
The following pages illustrate the calculations involved in the K-S test for the theoretical
probability distributions for the drought duration series of the Rio Grande at Del Norte, CO. The K-S
calculations compare deviations between the sample and theoretical cumulative density functions.
Similar tests were performed for all six headwater gages.
Analysis of Drought Severity vs. Drought Duration. With the probability distributions for drought
durations at the unimpaired gaging stations characterized, the relationship between drought severity
(defined as average cumulative drought deficit) and duration (number of years a drought event lasts) was
analyzed using linear regression techniques in Microsoft Excel. These analyses then complete the picture
concerning the behavior of droughts, relative to annual streamflow, at the unimpaired gaging points in
the Rio Grande Basin. It should be noted that, for each station, the correlation coefficient for the drought
duration and deficit series was calculated using the CORREL function in Microsoft Excel in order to
measure linear dependence between the two series.
From the probability distribution that best fit the drought duration series, the durations at which
the cumulative probability, P(x), was equal to 0.98 and 0.99 represented the 50-year and 100-year
droughts, respectively. These durations were then matched to the 50-year and 100-year deficits based on
51
the linear regression. The 50-year and 100-year drought durations and deficits were identified. A part of
the information concerning the relationship of drought duration to drought deficit for the Rio Grande is
shown below in Table 3-11.
Table 3-11. Sample of Rio Grande Drought Durations vs. Water Deficits
Regression Statistics Regression Plot Series
Multiple R 0.847 Drought Duration Drought Deficit(cfs-yrs)
R2 0.717 1 964,976Adjusted R2 0.716 2 1,929,952
Standard Error 6,574,162 3 2,894,928Observations 1297 4 3,859,904
Intercept 0 5 4,824,880X Variable 1 964,976 6 5,789,856
8 7,719,808
9 8,684,784
10 9,649,760
Estimation of 50-year and 100-year Droughts at Unimpaired GagesFifty and one-hundred year drought scenarios are shown for each of the six headwater gages in
four tables below. Table 3-12 shows annual values of total streamflow for 50-year drought scenarios, in
total water production, cfs-years. The 50-year drought duration of longest duration is for the Rio Grande
at Del Norte, CO, at 38 years. The shortest duration 50-year drought is for the Rio Puerco near Bernardo
NM, at 25 years.
Table 3-13 shows total cumulative storage deficits as defined previously for each year at each of
the six headwater gages. The drought is defined as ending when total storage deficit falls to zero.
Tables 3-14 and 3-15 show similar drought scenarios and storage deficits for the 100-year
droughts. The longest duration 100-year drought occurs for the Rio Grande at Del Norte, CO and Rio
Salado near San Acacia, at 47 years, while the shortest duration is for the Rio Puerco near Bernardo, NM
at 28 years.
3In this table and the following three tables, Conejos River flows include the Mogote gage only. The two othersignificant gages on the Conejos, for the Rio Grande Compact, are the Los Pinos and San Antonio. Drought scenariosfor the sum of the three index gage flows can be estimated based on these tabled flows. Based on the period 1941-1985,multiplying flows at the Mogote gage by 0.375 explains 98.5 percent of the variance in Los Pinos gage flows.Multiplying Mogote gage flows by 0.088 explains 93.4 percent of the variance in San Antonio gage flows. So,multiplying Conejos column flows in this table by (1 + 0.375 + 0.088) = 1.463, produces drought scenarios for the threeConejos River index gages. Average total flow of the three Conejos Index flows, in acre feet per year, is computed as119,485 (from the table) x 1.463 (three index flows based on Mogote flows) x 1.9837 (annual acre feet per cfs), whichis just under 347,000.
52
Table 3.12. 50-Year Drought Scenarios, Six Headwater Gages, Rio Grande Basin, Total AnnualStreamflows, in cfs-years.
RioChama
Rio Grande Rio Salado ConejosRiver3
Rio Puerco Jemez River
Ave flow 175,791 332,508 5,122 119,485 16,428 29,080
Criticalflow
131,844 249,381 3,841 89,613 12,321 21,810
Year
1 78,802 81,263 1,123 53,465 7,783 2,491
2 140,210 8,234 1,121 59,411 15,634 11,562
3 38,741 2,053 5,868 25,632 8,059 19,447
4 35,147 577,582 3,719 55,692 12,319 22,227
5 53,473 129,288 2,625 93,017 12,502 20,327
6 107,666 77,197 4,988 90,033 5,188 6,749
7 358,023 376,162 4,004 147,041 6,894 6,239
8 1,521 59,047 1,994 32,253 12,674 19,825
9 158,821 138,692 1,529 85,445 12,456 22,350
10 38,237 269,495 5,910 43,147 6,522 66,705
11 119,968 430,264 7,836 65,276 19,578 17,763
12 67,014 219,778 5,338 30,948 5,515 10,259
13 88,876 242,119 904 52,051 11,459 7,467
14 60,599 242,401 3,339 191,456 3,633 32,948
15 257,241 243,592 1,477 132,977 2,590 4,998
53
16 50,093 171,531 613 130,028 39,282 7,367
17 31,230 434,976 4,854 81,218 9,319 6,186
18 88,746 13,195 5,352 76,170 19,417 17,276
19 70,476 131,570 1,324 115,966 2,136 8,123
20 85,132 160,383 7,430 60,162 13,367 13,937
21 228,216 38,190 7,400 11,906 12,981 51,535
22 23,244 162,823 193 116,316 4,989 61,055
23 51,960 263,015 1,080 1,571 22,685 7,465
24 229,734 51,287 3,190 133,033 3,225 2,535
25 279,495 1,125,814 2,628 161,830 63,622 18,005
26 230,649 107,771 242 92,710 9,818
27 181,442 514,983 916 215,203 50,503
28 74,544 522,610 2,986 126,911 109,198
29 27,986 235,306 9,117 334,250
30 96,276 359,288 4,251
31 187,839 15,949 2,162
32 1,031,389 48,697 6,995
33 303,632 5,045
34 9,167 8,987
35 72,031 4,233
36 36,062 12,628
37 164,073
38 1,611,490
54
Table 3-13. 50-Year Drought Scenarios, Six Headwater Gages, Rio Grande Basin,Cumulative Storage Deficits, cfs-Years, Since Drought Onset.
Year Rio Chama Rio Grande Rio Salado RioConejos
Rio Puerco Rio Jemez
1 78,802 168,118 2,719 36,149 4,539 19,320
2 140,210 409,265 5,440 66,351 1,225 29,568
3 38,741 656,593 3,415 130,334 5,488 31,932
4 35,147 328,391 3,538 164,255 5,490 31,515
5 53,473 448,484 4,755 160,852 5,309 32,998
6 107,666 620,668 3,609 160,433 12,443 48,059
7 358,023 493,887 3,446 103,006 17,870 63,631
8 1,521 684,221 5,294 160,366 17,518 65,617
9 158,821 794,909 7,607 164,536 17,383 65,077
10 38,237 774,794 5,539 211,002 23,183 20,183
11 119,968 593,911 1,545 235,341 15,926 24,230
12 67,014 623,514 49 294,006 22,732 35,781
13 88,876 630,776 2,987 331,570 23,594 50,125
14 60,599 637,756 3,490 229,728 32,282 38,987
15 257,241 643,545 5,856 186,365 42,013 55,799
16 50,093 721,394 9,084 145,951 15,053 70,242
17 31,230 535,799 8,072 154,346 18,055 85,867
18 88,746 771,985 6,562 167,791 10,958 90,401
19 70,476 889,795 9,080 141,438 21,144 104,088
20 85,132 978,793 5,492 170,890 20,098 111,962
21 228,216 1,189,984 1,934 248,598 19,439 82,237
22 23,244 1,276,542 5,582 221,896 26,771 42,993
23 51,960 1,262,907 8,344 309,939 16,408 57,338
24 229,734 1,461,001 8,996 266,520 25,503 76,614
55
25 279,495 584,568 10,210 194,305 0 80,418
26 230,649 726,178 13,810 191,208 92,411
27 181,442 460,576 16,735 65,619 63,718
28 74,544 187,347 17,591 28,323 0
29 27,986 201,422 12,316 0
30 96,276 91,515 11,906
31 187,839 324,946 13,586
32 1,031,389 525,630 10,433
33 0 471,378 9,230
34 711,592 4,085
35 888,941 3,694
36 1,102,260 0
37 1,187,567
38 0
56
Table 3-14. 100-Year Drought Scenarios, Six Headwater Gages, Rio Grande Basin, TotalAnnual Streamflows, cfs-Years.
RioChama
RioGrande
RioSalado
RioConejos
Rio Puerco Rio Jemez
Ave. Flow 175,791 332,508 5,122 119,485 16,428 29,080
Critical Flow 131,844 249,381 3,841 89,613 12,321 21,810
Year
1 34,914 53,472 1,775 18,058 12,071 6,181
2 113,412 71,100 3,140 141,815 8,858 25,011
3 37,522 70,618 3,933 60,491 5,155 5,462
4 46,005 388,368 2,929 79,026 4,898 37,988
5 184,885 137,318 3,746 49,787 13,996 13,600
6 81,394 152,001 5,710 16,175 7,986 10,060
7 23,395 155,365 2,805 21,322 6,989 46,650
8 66,080 247,501 1,320 5,605 7,062 15,514
9 58,117 150,309 1,191 25,782 8,347 8,582
10 95,318 154,929 702 205,190 5,604 14,226
11 82,786 512,305 5,187 119,105 6,599 4,495
12 157,282 112,820 3,522 122,868 20,933 14,419
13 7,733 85,989 4,748 157,710 16,945 20,162
14 16,938 15,139 535 50,224 9,495 35,710
15 58,903 113,448 5,793 33,837 5,522 17,846
16 258,787 92,165 1,159 80,422 48,023 25,331
17 13,898 138,730 6,136 73,569 6,179 19,526
18 16,172 281,916 1,621 169,065 11,915 25,153
19 69,306 54,091 5,472 92,098 18,147 7,704
20 214,488 585,657 2,741 21,774 6,681 6,017
21 45,320 135,331 1,750 103,725 25,477 52,655
22 153,904 411,166 274 15,258 6,267 3,813
57
23 167,256 490,052 7,251 37,694 2,310 43,115
24 272,000 180,391 7,430 118,690 4,806 50,027
25 373,948 351,569 2,912 36,745 15,577 25,928
26 194,894 251,415 679 77,218 9,364 9,089
27 211,630 183,559 7,888 21,017 6,741 30,795
28 6,560 293,275 4,492 367,939 52,518 22,121
29 179,814 12,241 4,035 131,245 14,244
30 51,902 372,304 690 28,917 18,524
31 164,592 234,222 10,187 23,730 19,577
32 67,032 204,214 3,321 36,029 7,359
33 389,769 689,689 2,331 92,222 32,106
34 20,420 620,910 875 212,936 42,594
35 22,692 38,468 3,528 451,619 32,924
36 216,709 20,629 1,287
37 9,650 1,026,553 6,290
38 79,099 276,608 4,349
39 262,736 87,166 5,325
40 822,940 155,564 4,301
41 567,731 8,282
42 213,582 2,755
43 55,354 1,777
44 201,584 7,339
45 127,084 163
46 484,593 10,408
47 885,320 8,331
58
Table 3-15. 100-Year Drought Scenarios, Six Headwater Gages, Rio Grande Basin,Cumulative Storage Deficits, cfs-Years, Since Drought Onset
Rio Chama Rio Grande Rio Salado Rio Conejos Rio Puerco Rio Jemez
Ave. Flow 175,791 332,508 5,122 119,485 16,428 29,080
Critical Flow 131,844 249,381 3,841 89,613 12,321 21,810
Year
1 96,929 195,909 2,067 71,556 251 15,629
2 115,361 374,189 2,769 19,354 3,714 12,428
3 209,682 552,952 2,678 48,477 10,880 28,777
4 295,521 413,964 3,591 59,066 18,303 12,599
5 242,480 526,027 3,687 98,893 16,629 20,809
6 292,929 623,407 1,818 172,331 20,964 32,559
7 401,377 717,423 2,856 240,624 26,296 7,720
8 467,142 719,302 5,378 324,632 31,556 14,016
9 540,869 818,374 8,029 388,465 35,530 27,245
10 577,394 912,826 11,169 272,889 42,247 34,829
11 626,452 649,902 9,824 243,397 47,970 52,145
12 601,013 786,462 10,144 210,144 39,359 59,536
13 725,124 949,854 9,237 142,048 34,735 61,184
14 840,030 1,184,096 12,544 181,438 37,562 47,285
15 912,971 1,320,029 10,593 237,214 44,362 51,249
16 786,028 1,477,245 13,276 246,406 8,660 47,729
17 903,974 1,587,895 10,982 262,451 14,803 50,013
18 1,019,646 1,555,359 13,203 183,001 15,209 46,670
19 1,082,184 1,750,649 11,573 180,516 9,384 60,777
20 999,540 1,414,373 12,674 248,356 15,024 76,570
21 1,086,063 1,528,422 14,766 234,246 1,869 45,726
22 1,064,003 1,366,637 18,334 308,602 7,924 63,723
59
23 1,028,591 1,125,965 14,925 360,523 17,935 42,419
24 888,434 1,194,955 11,337 331,447 25,450 14,203
25 646,330 1,092,766 12,267 384,315 22,194 10,085
26 583,279 1,090,732 15,430 396,712 25,152 22,806
27 503,492 1,156,553 11,384 465,308 30,732 13,821
28 628,776 1,112,659 10,734 186,983 0 13,510
29 580,806 1,349,799 10,541 145,352 21,076
30 660,747 1,226,875 13,693 206,049 24,362
31 627,999 1,242,034 7,348 271,933 26,595
32 692,810 1,287,201 7,870 325,518 41,046
33 434,885 846,893 9,380 322,910 30,751
34 546,308 475,364 12,347 199,588 9,967
35 655,460 686,276 12,660 0 0
36 570,594 915,028 15,215
37 692,788 137,856 12,767
38 745,533 110,629 12,259
39 614,640 272,844 10,776
40 0 366,660 10,317
41 48,310 5,877
42 84,109 6,964
43 278,135 9,029
44 325,932 5,532
45 448,229 9,211
46 213,017 2,645
47 0 0
4Considerably more detailed analysis was done for Colorado than for New Mexico or west Texasagriculture. A Ph.D. dissertation completed at Colorado State University focused exclusively on San LuisValley agriculture (Sperow, 1998). In it the author developed detailed data sources and empirical relationsregarding water use and crop production. By contrast, relations regarding crop production and water use arescarce in New Mexico and west Texas. Also the New Mexico-Texas section of the study required analysisof three irrigation districts, while detailed analysis in Colorado focused on one.
60
Economic Analysis of Farm Response to Drought in the San Luis Valley, Colorado4
SummaryAn optimization model was developed that estimates net returns from cropping activities in the
San Luis Valley, Colorado based on available surface and groundwater for agriculture. Results of the
analysis indicate that crop production activities depend more on available groundwater than on surface
water diversions from the Rio Grande.
IntroductionAgriculture accounts for nearly 90% of consumptive water use in the western United States
(Gibbons 1986). Agricultural producers continue to experience increased competition for limited water
resources with growing urban populations. Brajer and Martin (1990) state that water is not becoming
scarce, but rather cheap water is becoming scarce as water markets develop.
Agricultural producers adapt to increased groundwater pumping costs, higher market values for
voluntary water transfers, and environmental constraints on water through improved irrigation efficiency
and reduced consumption (Moore, et. al. 1992). Surface water, with flows that are uncertain from year to
year and groundwater from aquifers with declining water levels, represent the primary source of
irrigation water for agricultural production. Sustained and severe drought conditions impact surface and
groundwater supplies, adding an additional element of uncertainty to agricultural production.
Most institutional arrangements for water allocation in the west are based on the Doctrine of
Prior Appropriation whereby the first person or organization that puts water to a beneficial use obtains a
61
decree amount and the highest priority right to that water through adjudication in water courts where
they exist. The Doctrine of Prior Appropriation is said by some economists to be economically
inefficient because it fails to promote water conservation in the face of growing scarcity (e.g., Burness
and Quirk 1979). In general, water markets that could, in principle, allocate water to higher economic
valued uses are poorly organized. So market signals that have the potential to promote higher economic
valued end uses are weak. Brajer and Martin (1990) contend that water is a social good and vital
necessity with attributes beyond its commercial value, so it should not be treated as a normal commodity.
Much of the current competition for water in the San Luis Valley of Colorado comes from
increasing urban populations along the Front Range that seek additional water sources. The competition
for water in southern Colorado is much the same as in the case of New Mexico and Texas, additional
water is needed to meet growing demands for uses outside agriculture, including endangered species
habitat. Irrigated agriculture could provide a source for transferring water supplies to meet these growing
demands since it typically absorbs the greatest amount of water in its use, and is of low economic value
at the margin for many crops. The value of water to agricultural production and how agricultural
producers respond to decreased water supplies in the face of drought by changing the mix of crops
produced is an important issue in the west for water policy analysis.
This section of the report develops a model that simulates the Doctrine of Prior Appropriation in
Colorado, identifies producer response to restricted water supplies, and estimates the value of water to
agriculture in the study area. This study provides a foundation for studies into the relaxation of
institutional constraints by developing an analytical method for identifying the value of irrigation water
for agricultural production. The area of study is the Closed Basin portion of the San Luis Valley in south-
central Colorado. The primary focus of the study is on changing surface water flows, however an
extensive aquifer is also accounted for in the analysis. A model addressing the major surface and
groundwater hydrologic features and the cropping patterns of producers in the region is developed. By
62
analyzing income changes due to low-water flows, the value of irrigation water to agricultural production
in the study area may be determined.
BackgroundRio Grande flow at the Colorado-New Mexico state line depends on snowpack, administration of
the Rio Grande Compact, and behavior of Colorado agricultural producers. What ends up at the
Colorado-New Mexico state line at the Lobatos gage depends on streamflow at Del Norte, Colorado, the
amount of water diverted for agriculture in Colorado, and the delivery requirements specified in the Rio
Grande Compact of 1938. The Rio Grande water has been over-appropriated. That is, more water has
been allocated to users than is generally available from the river. Junior rights may not receive water
during the growing season when surface water flows are low because senior rights, especially Rio
Grande Compact requirements, take precedence.
The San Luis Valley in Colorado consists of approximately 3,200 square miles with an average
elevation of about 7,700 feet. The Valley receives more water than most deserts in the country. The
average annual rainfall is 7 to 10 inches, with more than half of the precipitation occurring between July
and September. Crop production is difficult without supplemental water for irrigation. The short growing
season of 90-120 days also limits the choice of crops (Doesken and McKee 1989).
Conjunctive use of surface and groundwater provides the water necessary to irrigate crops in the
San Luis Valley. Groundwater in the San Luis Valley is obtained from an Unconfined Aquifer and a
deeper confined aquifer, which are separated from another confined aquifer by a series of clay
formations 10 to 700 feet thick. The study area is in the northern portion of the Valley that is referred to
as the Closed Basin because it is internally drained. An alluvial divide prevents water in the Closed Basin
from draining into the Rio Grande. Irrigation water diverted from the Rio Grande or pumped from the
63
aquifer within the Closed Basin that is not consumed by evapotranspiration does not return to the Rio
Grande, but recharges the Unconfined Aquifer within the Closed Basin.
Econometric (Nieswiadomy 1985; Ogg and Gollehon 1989; Moore and Negri 1992) and
mathematical (Bryant et. al. 1993; Kulshreshtha and Tewari 1991) techniques have been used to describe
water use by agricultural producers and to derive the value of water to crop production. Existing models
that address river diversions for agriculture have excessive data requirements and many do not consider
the Doctrine of Prior Appropriation. Wurbs and Walls (1989) developed a model that addresses prior
appropriation by accounting for water rights assigned to reservoir storage facilities in Texas. Bredehoeft
and Young (1983) analyzed a river basin delivering water to a single irrigation ditch for three areas with
hypothetical rights and decrees allocated. A mathematical model is developed for the analysis that
explicitly accounts for the Doctrine of Prior Appropriation, that is, economic returns from water are
maximized subject to priorities defined by seniority of water rights.
AnalysisThe economic value of water to the San Luis Valley is determined using a two-stage
optimization model that accounts for river flow, groundwater pumping, and effective rainfall. The
Doctrine of Prior Appropriation is addressed in the first stage of the model to allocate river water from
the Rio Grande to the irrigation ditches and canals holding the highest priorities. Rio Grande Compact
requirements are calculated outside the model so all river flow within the model may be diverted for
agricultural production. Municipal and industrial uses are not considered in the analysis because
agriculture accounts for 97% of water use in the San Luis Valley. The amount of water diverted
represents the amount of water available for crop irrigation. The area includes eight storage reservoirs
that provide some water for agricultural production, but are not considered in the analysis because they
are small and have junior water rights. Cropping and irrigation decisions are dependent upon the amount
64
of surface water that is available and whether groundwater rights are owned by the producer. Cropping
patterns and the associated net returns from irrigation water are estimated in the second stage of the
model based upon crop production functions and costs of production for the primary crops produced in
the study area.
The impact of decreased water supplies on crop production is analyzed by parametrically
decreasing the amount of river flow and volume of available aquifer water and estimating the change in
the value of crop production. The proportion of groundwater in the aquifer that may be pumped
economically is not known with certainty. By parametrically decreasing available groundwater and
surface water, the relative importance of groundwater pumping and surface water sources will be
identified.
The Colorado Division of Water Resources has partitioned the state into seven water divisions
organized around major drainage basins or series of rivers. The Rio Grande is in Water Division Three.
River flow and diversion records are maintained by Water Districts, representing river basins. The San
Luis Valley has six Water Districts with Water District 20 representing the Rio Grande Basin. The Rio
Grande accounts for 70.1% of diversion rights in Water District 20 where 91 other sources (creeks and
streams) also provide water. The Rio Grande accounts for 337 of the 861 water rights in Water District
20. Historical diversion records indicate that the Rio Grande accounted for over 93% of actual diversions
from 1986 to 1995 in Water District 20. Simulating cropping activities that divert water from the Rio
Grande is sufficient to account for most of the water diverted for irrigation in the Closed Basin.
Irrigation ditch/canal companies own the water rights in the San Luis Valley and producers own
shares, each of which receives the same amount of water. Each ditch/canal company owns a suite of
water rights with different priorities and decree amounts. Water right, decree amount, geographic
location, and decree date were obtained from the Colorado Division of Water Resources. Five irrigation
ditches/canals are included in the simulation - four actual irrigation ditches/canals and one to account for
65
diversions to cropping activities outside the study area. Cropping activities are simulated only for
representative agricultural areas along the four irrigation ditches/canals explicitly included in the model.
Four of the 101 irrigation ditches on the Rio Grande account for over 60% of water rights within the
study area. Explicitly included in the simulation model are the Rio Grande Canal, Farmer’s Union Canal
(now the San Luis Valley Irrigation District), Prairie Ditch, and the San Luis Valley Canal.
Table 3-16 identifies the number of acres serviced by each of the four irrigation ditches in 1995,
the number of shares held by each ditch and the annual assessment for diverting water from the ditch. All
other ditches are combined into a single diversion "ditch" with the priority and decree amount of
individual diversions maintained.
Table 3-16. Canals / Ditches Modeled in the Analysis, Acres Serviced by Canal/Ditch, Numberof Shares Held by the Canal/Ditch, and Annual Assessment for Each Share, San Luis ValleyColorado.
Canal/Ditch Acres Number of shares Assessment Prairie Ditch 13,196.40 250 $300/shareRio Grande Canal 75,701.90 7152.825 $60/shareSan Luis Valley Canal 10,051.50 13280 $7.50/shareSan Luis Valley Irrigation District 7,933.10 388a $1200/quarter-section
a The ditch does not use shares, but services 388 quarter-sections. Landowners serviced by the ditch get an equal shareof the water if they call for it.
The five canals/ditches represent the nodes addressed in the river flow model where water is diverted
from the river. Figure 3-5 is a schematic of the Rio Grande with the irrigation ditches and canals
included in the simulation model. Crop production is simulated for representative agricultural areas that
divert irrigation water from the four irrigation ditches explicitly included in the simulation model.
5Many of these assumption necessarily simplifies reality. For example, water often moves more easily throughthe aquifer than these assumptions suggest. It would be highly desirable to develop a detailed hydrological model ofthe Valley that accounts for relevant interactions between aquifer size, shape, and characteristics, groundwater pumping,snowmelt, surface water supplies, surface water diversions, crop production, and crop return flows.
66
Groundwater in the study area is pumped from the unconfined aquifer that lies mostly below the
north half of the Valley. Precise data for the amount of water in the aquifer are not available, but are
estimated for this study. The depth to the blue clay series that separates the Unconfined from the
Confined Aquifer represents the depth of the Unconfined Aquifer. This depth changes from north to
south and west to east in the study area.
For analytical purposes, several assumptions were made.5 The Unconfined Aquifer was divided
into nine separate cells determined by the depth to the blue clay series, with each aquifer cell treated as a
67
bowl containing an amount of groundwater dependent upon its volume. Water does not move between
aquifer cells in the model during the cropping season. Recharge from drainage and recharge pits
percolates only into the aquifer below where crop production is occurring. Aquifer recharge occurs from
percolation from irrigation ditches and canals, watershed runoff, precipitation, and leakage from artesian
wells. Two-thirds of aquifer recharge occurs during the cropping season and is allocated equally to each
aquifer cell in the model. At the start of each simulation, a quantity of water is allocated to the nine
aquifer cells in a way consistent with the movement of recharge water across the Valley. That is, each
aquifer cell is allocated an amount of water equal to its share based upon the depth and holding capacity
of the cell. Since water flows to the lowest point, the deepest aquifer cells receive water first and others
receive water only if there is sufficient water.
The specific yield for most portions of the aquifer is approximately 0.20, which is used in this
analysis (Emery 1970; Woodward-Clyde-Sherard and Associates 1967). In general, the aquifer locations
cover areas from northwest to southeast with surface areas that range from 4,480 to 65,920 acres. The
amount of water simulated in the nine aquifer cells (2.46 million acre-feet) compares well with other
estimates of the Unconfined Aquifer (Woodward-Clyde-Sherard and Associates 1967).
Most producers in the study area do not apply surface water directly to their fields, but rather
divert the water to holding ponds (known as recharge pits), which recharge the aquifer. Most water
diverted to recharge pits percolates to the aquifer, but is not available for pumping until the next time
period. The aquifer is also recharged through inefficient irrigation of applied water by crops. The amount
of aquifer recharge from surface and groundwater sources is dependent upon the irrigation technology
used. In the Closed Basin, all irrigation is done by relatively new center pivot equipment. Therefore,
recharge rates are considered to be the same on each representative farm.
Thirty-three representative agricultural areas were used to simulate crop production along each
of the irrigation ditches/canals included in the analysis. Representative agricultural areas were
68
determined by the soil characteristics, source of surface water used for irrigation (ditch/canal), and
groundwater source. The 47 primary soil types in the study area range from clay loam to gravelly sandy
loam. These were partitioned into sand and sandy loam soils for the crop simulation model. These two
soils account for a majority of the variation in soil characteristics. Representative agricultural areas were
restricted to diverting surface water from a single irrigation ditch/canal and could pump groundwater
from only the aquifer cell beneath the farm. Equipment and financial status of most farms in the Closed
Basin are similar and were treated as such in the model. Farms within the study area were assumed to be
price takers because the amount of production for any crop does not influence national prices. Even
though Colorado is one of the leading producers of potatoes in the country, San Luis Valley production
of this crop represents only 6% of national production. Alfalfa represents 4% of the national production
and barley 2.7%.
Data were obtained on historic crop acreage for grain (primarily barley and spring wheat),
potatoes, and alfalfa on each quarter section in the study area from 1983-1994, the primary crops
produced. Malting barley is often grown with contracts from the Coors Brewing Company, but the higher
prices received were not considered in the analysis. The seed variety most frequently grown (Moravian
III) for both brewery contracts and feed is the same. Some vegetable crops, particularly carrots, lettuce
and peas are gaining popularity, but are not considered primary crops so were not addressed in the
analysis. Land around the periphery of the valley floor is used for grazing cattle, but cattle operations
were not considered in the analysis.
The model was calibrated using river flow data for ten years for the Rio Grande at Del Norte, the
headwater gage on the Rio Grande. The baseline model results for diversions and cropping patterns were
compared to historic stream flows, diversions and cropping patterns to ensure that reasonable results
were obtained.
69
Hydrology Model DevelopmentA mass balance river flow model that diverts water by priority and decree amount was developed
in GAMS (Brooke et. al. 1988). The model identifies diversions that maximize the total amount of water
diverted while satisfying each decree by priority. When river flow is insufficient to satisfy all users,
junior decrees are not provided water. Water available from each irrigation canal/ditch is used in the
second stage of the model to simulate crop growth and estimate the value of crop production.
Five equations establish the constraints and water allocation amounts. First, diversions at each
node must be less than or equal to the decreed water right held by the ditch at that node for each time
period and must also be less than or equal to the amount of water in the river as shown in Eqs. 3.18a. and
3.18b. River flow is simulated for six time periods to account for the cropping season.
(3.18a)Divert Water right i ti,t i≤ = − = − 1 123 1 6;
(3.18b)Divert Flowi t i t, ,≤where i is the right (i = 1-123), and t is time (t = 1- 6)
To simplify the analysis, water rights for ditches with consecutive priorities were grouped together and
considered a single water right with a single priority, which reduced the total number of water rights
from 337 to 123. That is, when a single irrigation ditch or canal owned priority numbers 1, 2 and 3, they
were combined to priority 1 with a diversion right equal to the sum of decrees for the three rights.
Second, river flow at the first node is the same as the constant entered into the model as the flow
for that time period. At the second and subsequent nodes, river flow is reduced by the amount of water
diverted by upstream ditches (Eqs. 3.19a and 3.19b).
70
(3.19a)Flowi t Inflow t for i t, , ;= = − = −1 123 1 6
(3.19b)Flow Flow Diverti t i t i t, , ,= − −1 1
Third, the highest priority ditches receive water before more junior priorities, even when the
higher priority ditch is geographically located downstream from the junior priority. The objective of the
first stage of the model is to maximize the total amount of water diverted to irrigation ditches constrained
by the priority and decree amount of each irrigation ditch using Eq. 3.20. This weighted equation limits
diversion of water at any upstream ditch to zero in each time period if there are downstream ditches with
higher priorities and river flow is not sufficient to satisfy all rights.
(3.20)Objective = Priority * Diverti=1
123
i2
i,t∑ ∑=
11
6/
t
Equation 3.21 is used to identify the irrigation ditch receiving water and the amount of water
diverted for each right.
(3.21)Ditch Divert for each Owner Ditch IDl,t i,tI 1
123
i i = ∑ ==
The volume of water in the aquifers is dependent upon the initial condition, quantity of water
added from recharge pits, drainage of water not consumed by crops and the amount of water removed
through pumping activities. Water added through recharge pits is positive when a representative farm
diverts water from an irrigation ditch/canal. That is, to ensure all surface water is used in the analysis, to
reflect operations in the San Luis Valley, all water diverted from an irrigation ditch/canal is used by the
representative farm, either in recharge pits, or surface applied to a field by flood irrigation. Since all
cropping activities in the study area use center pivot irrigation systems, a charge is assessed for flood
irrigation activities to artificially force use of recharge pits. The amount of surface water available, water
71
from irrigation ditches/canals less the amount of water surface applied, represents the amount of water
applied to recharge pits.
Water not used by plants ("Drain") is calculated using Eq. 3.22.
(3.22)Drain = M = 1
33(1 ETA ) * Wapplied * RtnFracq,t M M,t M,q∑ −
Where:
Drain = amount of water seeping into aquifer
q = aquifer identifier (1-9)
t = time periods (1-6)
M = farm (1-33)
ETA = irrigation efficiency by farm
Wapplied = amount of irrigation water applied to crops, and
RtnFrac = proportion of non consumption returning to aquifer.
Pumping costs are included in the variable costs and are applied at a rate of $37.50 - $40.00/acre-
foot for all representative agricultural areas while costs to apply surface water are much lower, estimated
at $5/acre-foot.
Bredehoeft and Young (1983) found that the optimum capacity for wells in their study area (the
Platte River Valley of Colorado) was about one-half the capacity of wells actually installed. Increased
well capacity provided insurance against low-river flows, reduced the variance of expected income, and
maximized expected income. Pumping rights are required to remove water from the aquifer in the study
area of the San Luis Valley. Average well capacity in the region is 900-1000 gallons/minute. Estimated
pumping capacities for some farms in the study area were higher than crop requirements, but
72
groundwater rights are frequently less than pumping capacity. Representative agricultural areas were
constrained to pumping no more than the minimum of the groundwater right plus the amount of recharge
from recharge pits, the farm pumping capacity, or their proportion of the amount of water remaining in
the aquifer. The farm proportion of aquifer water is based upon their proportion of total surface area
above the aquifer.
Crop Growth Simulation ModelA crop growth simulation model was used to develop coefficients for the optimization model
production functions (Cardon 1990). Second and third order polynomial equations, depending upon the
crop, represent the results of the crop growth simulation model better than other functional forms.
Equation 3.23 describes the general form of the crop growth function used for all crops to derive the
relative yield variable:
(3.23)Y a bX cX dX= + + +2 3
Where: Y = relative yielda = intercept coefficientb = slope coefficientX = amount of water applied (acre inches)c = slope coefficient, andd = slope coefficient.
Relative yield, Y, is constrained to be less than or equal to one in the model because production
functions for all crops do not have a global maximum. Coefficients (Table 3-17) for crop growth
functions were derived through regression analysis of data from the crop growth simulation model. The
model employs a daily time-step to simulate the relationships between water and soil, water and plant
growth and yield, and evapotranspiration to derive relative yield parameters based upon water available
for plant growth. It simulates water movement through the soil profile and water uptake by the plant. Site
73
specific input files were generated to reflect growing conditions and hydraulic properties of soils in the
study area (Rawls 1992; U.S.D.A. 1988). Crop growth was simulated with the number of irrigation
events varying from 0 to 24 for potatoes (fewer irrigations for alfalfa and barley) to generate production
functions for each crop. All nutrients except water were assumed adequate for normal crop production
and effective rainfall was included as a parameter.
Table 3-17. Crop Growth Coefficients for Crop Production Functions (Eq. 3.23)a b c d
Sandy SoilsAlfalfa 0.06106 0.12290 -0.00395 0.00000Barley 0.24736 -0.01420 0.00573 -0.00016Potatoes -0.01130 0.05690 -0.00080 0.00000Sandy Loam SoilsAlfalfa 0.48808 0.09000 -0.00389 0.00000Barley 0.38689 0.06960 0.02024 -0.00245Potatoes 0.40019 0.16650 -0.01585 0.00052
Total water applied to crops is determined using Eq. 3.24 and is constrained to be less than the
combined amount of surface water applied and pumped from the aquifer. Net irrigation is calculated
using Eq. 3.21 where irrigation efficiency of the irrigation system is addressed.
(3.24)Wapplied (Wapprate * Cropacre )M,t M,c,t M,c= ∑=c 1
3
Where: Wapplied = total amount of water applied to crops
M = farm (1-33)
t = time period (1-6)
c = crop (alfalfa, barley, potatoes)
Wapprate = a free variable determined by the model, and
Cropacre = number of acres planted to each crop.
74
(3.25)Nir Wapprate * EtaM,c M,c,tt 1
6
M= ∑=
12 *
where:
Nir = net irrigation amount
M = farm (1-33)
t = time period (1-6)
c = crop (alfalfa, barley, potatoes)
W apprate = a variable determined by the model, and
Eta = irrigation efficiency parameter
The objective of the second stage of the model is to maximize the sum of net returns from all
crops and farms in the study area. Moore, Gollehon and Carey (1994) determined that the choice of acres
on which to produce crops is the first decision made by producers and the cost of water was second.
Therefore, the costs for shares of irrigation ditch water are not included in the optimization, but are
subtracted from returns net of other variable costs. The coefficients for price and variable costs are
included in Table 3-18.
Table 3-18. Price and Variable Costs for Alfalfa, Barley and PotatoesAlfalfa Barley Potatoes
Price $85.00/ton $3.26/bu $5.50/cwtVariable Cost/Acre $129.60 $179.66 $596.12Variable Cost/Yield $24.25 $0.34 $0.12
Results and DiscussionThe first stage of the model identifies river diversions to irrigation ditches consistent with actual
diversions. Deliveries of 153,720 and 72,600 acre-feet are needed to satisfy Rio Grande Compact
requirements for 100% and 50% flow levels, respectively. The amount of water available for diversion is
75
423,964 acre-feet when river flow is 100% and 211,982 acre-feet when river flow is at 50% of normal.
The initial aquifer volume is 2,461,440 acre-feet, which declines to 1,230,720 acre-feet when the aquifer
is at 50% of capacity.
The crop production portion of the model accounts for over 88% of crop acreage for the base
year. Six of the seven representative agricultural areas lacking groundwater rights do not produce crops
when 100% of river flows are unavailable, regardless of available aquifer water. These agricultural areas
are included in the model to account for surface water diversions even though crop production does not
always occur. The model accounts for 100% of crop production on farms holding both surface water and
groundwater pumping rights.
The amount of water available from river flow for crop production, which is the amount of water
diverted to irrigation ditches/canals, is included in Table 3-19 for 100% and 50% flows for each
irrigation ditch/canal.
Table 3-19. Water Diversions for Each Irrigation Ditch/Canal with100% and 50% of River Flow Available
Ditch/Canal Amount of River Diversions (Acre-feet)100% River Flow 50% River Flow
1 77,302.2 44,889.62 16,630.5 0.03 13,923.7 1,071.04 11,053.2 0.05 305,054.4 166,021.4
The amount of water used for crop production on each representative farm, the irrigation ditch
from which water was diverted, total acres available for crop production, and the number of acres on
which crop production occurred are included in Table 3-20. A 50% decline in river flow and available
groundwater results in a reduction of 17,522 acres from full production of 144,973 acres when full water
is available. Seven of the 33 representative agricultural areas reduce crop production in response to
76
declining water supplies with 14,668 acre-feet less water applied to crops.
Acres producing alfalfa, barley and potatoes are included in Tables 3-21 through 3-23. Alfalfa
production remains constant as river flow declines. A 50% reduction in both groundwater and surface
water results in an 11% decline in alfalfa production. When there are no river flows and available water
in the aquifer is at least 50%, alfalfa production is decreased by 17% compared to the results when full
water is available from both groundwater and surface water sources.
Table 3-20. Representative Farm, Irrigation Ditch/Canal from which Water is Diverted,Acres Available for Crop Production, Acres Cropped, and Amount of Water Appliedwhen River Flow and Aquifer Volume are Full and Reduced by 50%
FarmDitch /Canal
AcresAvailable Acres Cropped
Water Applied to Crops(Acre-feet)
100% Flowand Aquifer
50% Flow andAquifer
100% Flowand Aquifer
50% Flow andAquifer
1 1 14,268 14,268 14,268 38,005 38,0052 1 11,316 11,316 11,316 28,693 28,6933 1 12,792 12,792 12,792 33,109 33,1094 1 13,776 13,776 13,776 36,439 36,4395 1 3,936 3,936 3,936 10,831 10,8316 1 3,444 3,444 3,444 2,811 2,8117 1 3,936 0 0 0 08 1 3,444 0 0 0 09 1 5,412 0 0 0 0
10 2 7,380 7,380 7,380 20,682 20,68211 2 2,952 2,952 2,952 7,082 7,08212 2 1,968 0 0 0 013 2 12,792 12,792 12,792 10,353 10,35314 2 2,952 2,952 0 2,416 015 2 3,444 3,443 3,443 2,794 2,79416 2 1,968 1,967 0 1,593 017 2 1,476 0 0 0 018 2 2,460 2,460 2,460 2,124 2,12419 2 2,460 2,460 0 2,161 020 2 1,968 1,968 1,968 5,083 2,28421 2 984 490 0 1,432 022 2 4,428 4,428 4,428 3,861 3,86123 2 3,444 3,444 3,444 2,602 2,60224 2 1,476 0 0 0 025 3 984 330 25 738 5726 3 984 984 984 2,893 2,89327 3 8,856 8,855 8,855 7,232 7,232
77
28 3 3,444 3,444 3,444 2,708 2,70829 3 4,428 4,428 4,428 4,164 4,16430 4 5,904 5,904 5,904 4,914 4,91431 4 7,380 7,380 0 6,227 032 4 2,952 2,952 2,952 2,338 2,33833 4 4,428 4,428 4,428 12,792 12,792
Table 3-21. Acres of Alfalfa Produced with DifferentQuantities of Water Available
Proportion of Proportion of River Flow (%)
Aquifer Available (%) 100 50 0----------------- Acres --------------
100 24,425 24,425 24,425
50 21,751 21,751 20,331
0 5,306 4,444 0
Barley production requires less water than either alfalfa or potatoes, but the value of barley as a
crop enterprise is less than either of the other two crops. To attain the highest net returns, production
should be shifted away from lower value crops to higher value crops when water becomes scarce. The
simulation model reflects the change in crop mix by reducing the amount of barley produced when water
shortages occur. A 50% reduction in surface and groundwater causes a 9.8% reduction in barley
production. Barley production is reduced by 33.3%, compared to production under full water availability
conditions, when no river flow is available and 50% of the aquifer is available. This decline is larger than
either the reduction in alfalfa or potato production, reflecting the shift away from lower value products
and applying water to higher value products.
78
Table 3-22. Acres of Barley Produced with DifferentQuantities of Water Available
Proportion of Proportion of River Flow (%)
Aquifer Available (%) 100 50 0
-----------------Acres--------------
100 64,996 59,245 63,961
50 58,622 58,622 43,329
0 6,877 4,576 0
Potatoes are the highest value crop in the study area. As the highest value crop, irrigation of
other crops should be reduced and the water applied to potatoes when river flows and available water in
the aquifer decline. Potato production declines by 13.1% when river flow and available groundwater are
reduced by 50%. When river flow is reduced to zero and 50% of aquifer water is available, potato
production declines by 12.9% compared to production with full river flow and aquifer levels. The
reduced potato acres is consistent with expectations when river flows are reduced to zero. Reduced acres
of potato production in the face of reduced river flow are small, as most river shortages are allocated to
grains and alfalfa, consistent with the high net income potential of potato production. However, the
proportion of total acres for each crop produced remains relatively stable with 100% compared to 50%
available surface and groundwater. Alfalfa production represents the same proportion (16.9%), barley
production increases slightly (from 44.8% to 45.5%), and potato production declines slightly (from
38.3% to 37.5% of all production).
Table 3-23. Acres of Potatoes Produced with Different Quantities of Water Available
Proportion of Proportion of River Flow (%)
Aquifer Available (%) 100 50 0
-----------------Acres--------------
100 55,552 55,247 55,222
50 48,585 48,280 48,367
0 5,858 5,553 0
79
Total net returns from crop production with river flow and available groundwater varied from
100% to 0% are shown in Table 3-24. When available groundwater from the aquifer remains at 100%,
reducing the river flow has only a minor impact on overall crop production. When river flow is reduced
to zero, net returns show an increase because shares for irrigation ditch/canal water are not purchased,
resulting in lower overall costs. Net returns are reduced $1.4 million when river flow is reduced by 50%,
but available water from the aquifer remains at 100%. When river flow is 100% and available aquifer
water is reduced by 50% net returns are reduced $10.7 million. When river flow and available aquifer
water are reduced by 50%, net returns are reduced by nearly $11 million. A 50% reduction in available
aquifer water is more costly than a 50% reduction in surface water, in the short run, by over $9.3 million.
Table 3-24. Total Net Returns from Crop Production with River Flow andAquifer Volume Declining from 100% to 0%
Proportion of Proportion of River Flow (%)
Aquifer Available (%) 100 50 0
------- Net Economic Value of Returns ($) --------
100 83,866,156 82,511,569 84,405,297
50 73,187,984 72,927,298 70,0799,34
0 9,841,168 8,235,602 0
ConclusionsThe results of this analysis show the importance of the unconfined aquifer to crop production in
the San Luis Valley and particularly in the study area. Net returns decline sharply when aquifer water is
depleted, but are relatively unaffected by declining river flows.
Rio Grande flows are, however, important for crop production and recharging the Unconfined
Aquifer. When river flow declines, irrigation diversions decline, and less water is available for aquifer
recharge. As long as there is significant river flow, crop production is somewhat unaffected until very
low flow levels occur. Net returns are $3.1 million higher when Rio Grande flows are 100% of normal
with 50% of the aquifer, compared to returns when river flow and aquifer volume are both 50% lower.
80
These results should be interpreted with caution because cropping decisions in a static single-season
simulation do not account for future events.
Recharge to the aquifer and allocation of water at the beginning of the simulation to each aquifer
cell, based upon its volume and depth, were accounted for in the simulation model. However, recharge is
allocated equally in each time period, and the movement of water between aquifer cells during the
cropping season is not addressed. Additional research is required to refine the aquifer dynamics for both
intra- and inter-year aquifer cells. Anecdotal evidence indicates that the aquifer cells should dry up from
east to west, an artifact of aquifer dynamics that is not addressed in a static single-season model.
More robust findings would result from a dynamic model that accounted for declining aquifer
levels in the cropping decisions by producers. The simulation model presented in this analysis can be
used to provide input data for a discrete dynamic programming model. In the model presented, producers
were free to deplete groundwater supplies because short-run decisions address only the current time
period and do not consider future production possibilities.
Documentation of Colorado Farm Drought Response ModelWater Rights and Supplies
Agriculture is the primary industry in the San Luis Valley (SLV) of Colorado where natural
precipitation is insufficient for producing most crops. Crop production in the SLV depends upon water
flow in the Rio Grande and groundwater supplies during the cropping season in the basin area. Surface
and groundwater are allocated by the doctrine of prior appropriation. A water right and priority are
established by an individual or organization that applies water to a "beneficial use". The water right is
maintained by continuing to use the water for the "beneficial use" for which the right was established and
obtaining a decree from the water court, which legally establishes the priority date and decree amount of
the water right. Irrigation ditch companies own surface rights for Rio Grande water. Producers own
shares of the ditch and are allocated water based upon the number of shares they own and the amount of
6Despite the low value of water in agriculture per acre-foot, many acre-feet of water are used in Colorado’sRio Grande Basin. In fact Colorado’s use of water in the San Luis Valley has made many millionaires.
81
water diverted to the irrigation ditch from the river. Each ditch share receives an equal amount of water
based upon the total number of shares issued by the ditch and the amount of water in the ditch, so when
river flows are low, all shares are affected equally. Groundwater rights are property of the well owner.
River diversions are controlled and monitored by the Division Engineer to ensure water is allocated
accurately to water right holders.
Water supplies in the SLV are threatened from two different sources. First, increased demands
for limited water supplies from metropolitan areas along the Colorado Front Range and nearby states are
threatening to change the historical use of water in the SLV. Growing urban populations of New Mexico
and Colorado are searching for additional sources of water for municipal and industrial uses. Over 97%
of the water in the SLV is applied to agriculture. Agricultural cost and return budget analysis typically
shows that on a per dollar per acre-foot basis, irrigated agriculture typically can afford to pay much less
than cities will pay for the same water.6
Second, the amount of water flowing in the Rio Grande is dependent upon the amount of
moisture accumulating as snow in the mountains over the winter. A sustained drought would impact river
flow and water storage in the Unconfined Aquifer, thus affecting agricultural production. The purpose of
this study is to provide decision makers, producers and water managers additional information about the
value of water to agricultural production in the SLV, a topic which has not been analyzed.
The impact of exporting water out of the SLV or a sustained drought would have the same effect
on agricultural production in the Valley - less water available for crop production. The analysis in the
main text addresses the response to a sustained drought, which provides the same results as decreased
water supplies from diversions to municipal and industrial uses outside the SLV.
7Important future research would examine water allocation on a daily basis. During the growing season, runoffexperiences wide daily changes.
82
The response to sustained drought in the SLV is analyzed by simulating changes in cropping
patterns and calculating the value of water by estimating the change in the value of crop production. A
two-stage nonlinear optimization model is developed in GAMS (General Algebraic Modeling System) to
allocate river water to irrigation ditches by priority and decree (Brooke, et al. 1988). The objective of the
first stage is to maximize the amount of water allocated to ditches dependent upon the amount of water
in the river. The first stage of the model allocates water to irrigation ditches based upon priority, decree
and river flow for growing season months (April � September). A monthly time step is used in the
GAMS model, so each simulation consists of six time periods.7
The objective of the second stage is to maximize the value of returns from crop production,
determined by simulating irrigation and cropping decisions, constrained by available water, soil type,
cropping history, and location. Cropping and irrigation decisions are based upon the amount of irrigation
water available for crop production that is represented by the amount of water diverted to irrigation
ditches from the river. The model identifies the changes in net returns from producing different crops
when water shortages occur. Acres allocated to each crop on each farm were based upon the ten-year
average of crops grown. Yields for each crop are derived from crop production functions generated by a
crop growth simulation model.
The GAMS model is included in the Appendix with the input files used by the GAMS model.
The remainder of this appendix includes a description of the optimization model that is not included in
Chapter 3, the sources of data, and identifies the data manipulations required to obtain the correct format
for successfully solving the model.
83
Selection of Water Source to SimulateThe Colorado Division of Water Resources has partitioned the state into seven water divisions
organized around major drainage basins or series of rivers. The SLV study area is in the Rio Grande
Basin designated as Water Division Three. Water divisions were historically subdivided into Water
Districts, a classification that is no longer practiced, although data are maintained by these designations.
The study area is in Water District 20, which contains 91 sources of water (rivers and streams) with 454
irrigation ditches and canals holding 861 water rights.
Simulating all the water sources and diversion nodes within the study area is too extensive to
include in a river flow model. The Rio Grande accounts for 337 of the 861 water rights and 101 of the
454 irrigation ditches and canals in the study area. When decrees without a priority assignment and
decrees for reservoir storage are not included, the Rio Grande accounts for 77.3% of all water decreed in
Water District 20. Water rights for reservoir storage are junior and represent a very small proportion of
total diversions from the Rio Grande. The most junior water rights are deleted from consideration
because they cannot be simulated. Since the Rio Grande accounts for most of the decrees in study area,
only irrigation ditches on the Rio Grande are simulated.
Six of the 101 irrigation ditches on the Rio Grande account for nearly 77% of diverted water
from the Rio Grande. These irrigation canals and ditches (Rio Grande Canal, Farmers Union Canal,
Monte Vista Canal, Prairie Ditch, San Luis Valley Canal, and the Empire Canal) account for a total of
56% of all diversions in Water District 20. The Rio Grande Canal, Farmers Union Canal, Prairie Ditch
and San Luis Valley Canal account for over 60% of Rio Grande diversions, are in the study area, and are
explicitly included in the model. The Monte Vista and Empire canals divert water from the Rio Grande,
but apply it to acreage south of the river. All other ditches are combined into a single diversion "ditch"
that maintains the priority and decree amount of individual diversions. The geographic location of the
84
five ditches (specifically the upstream-downstream relationship) is not relevant because the priority and
decree amount determine which ditches receive water. A downstream ditch with senior rights is allocated
water by the model ahead of a junior upstream user.
Irrigation Ditch/Canal Data AnalysisThe data were analyzed to determine if a limited number of ditches could adequately represent
water diversions in the study area and to determine the proportion of diversions in Water District 20
provided by the Rio Grande. The methods used to determine which water sources and irrigation ditches
to include in the model are identified in this section. The objective of the analysis is to identify the river
source providing the majority of water for diversion to irrigation ditches and identify the irrigation
ditches and canals that are likely to divert the majority of the water. The analysis in the remainder of this
section addresses the relationship between the decrees for the six largest irrigation ditches and "all other"
diversions to establish how representative the ditches included in the model are of all Rio Grande
diversions. The proportion of decrees allocated to the four irrigation ditches explicitly included in the
model can be derived from the tables.
Overall, Water District 20 contains 454 irrigation ditches with 17,707 cfs in decrees, based on
numerous complex decrees. Associated with these ditches are 861 total water rights. The 12,418 cfs in
decrees on the Rio Grande accounts for 70.1% of all decrees in Water District 20 (Table 3-25). Included
in these data are many decrees without a priority assignment and decrees for reservoir storage. Decrees
without a priority assignment are ignored because they cannot be simulated without arbitrarily assigning
a priority and their dates of appropriation are recent. River flow would have to be above normal to satisfy
these decrees. Above normal flows are not considered in this analysis.
85
Table 3-25. Total Decrees from WD 20, Rio Grande andSix Ditches with Largest DecreesLocation Decrees (Cfs) % of WD 20Water District 20 17,707 100.0Rio Grande 12,418 70.1Top 6 Decrees 10,119 57.0
The six ditches with the largest decrees in Water District 20 that divert water from the Rio
Grande are included in Table 3-26 along with the decree amount. The six irrigation ditches and canals
account for 57% of all decrees in Water District 20.
Table 3-26. Irrigation Canals and Ditcheswith Largest Decrees in Water District 20Ditch Name Decree (Cfs)Rio Grande Canal 3,856Farmers Union Canal 2,111Empire Canal 1,526Prairie Ditch 1,101Monte Vista Canal 1,022San Luis Valley Canal 500
Decrees for reservoir storage are not relevant to the economic analysis that addresses allocation
of surface water to agricultural production. Six irrigation ditches contain decrees with no priority for
diversion to reservoirs and the appropriation and adjudication dates are very recent. The six ditches are
listed in Table 3-27 along with the amount of the decree, source of water, and appropriation/adjudication
dates. According to Colorado water law, the appropriation date establishes the priority of the decree.
These ditches are not considered in the analysis because they represent junior rights for reservoir storage
with no priority assignments. These ditches represent 3,950 cfs that do not need to be addressed in the
model. Removing the requirement to provide water to these ditches decreases the total decrees in Water
District 20 to 13,757 cfs (Table 3-28). Total decrees allocated to the Rio Grande are 11,868 cfs, or 86.3%
86
of all decrees for Water District 20. According to these data, using the Rio Grande as a representative
water source seems adequate because the Rio Grande accounts for nearly all the decrees in Water District
20.
Table 3-27. Water District 20 Reservoir Decrees with No Priority and Late Appropriation/Adjudication Dates Not Included in the River Flow Model
Ditch Name River Source Decree Amount(Cfs)
Appropriation/Adjudication Date
Continental ReservoirRio Grande Exchange
San Antonio 2,500 1968/1990
Santa Maria ReservoirRio Grande Exchange
San Antonio 350 1968/1990
Continental/SantaMaria Reservoir Exch.
San Antonio 300 1981/1990
Rio Grande/Santa Maria Reservoir Exch.
Rio Grande 300 1981/1990
Rio Grande/ContinentalReservoir Exchange
Rio Grande 250 1983/1990
Santa Maria/ContinentalReservoir Exchange
San Antonio 250 1964/1990
Table 3-28. Total Decrees from WD 20, Rio Grande andSix Ditches with Largest Decrees after Decrees Listed inTable A.2 DeletedLocation Decrees (cfs) % of WD 20Water District 20 13,757 100.0Rio Grande 11,868 86.3Top 6 Decrees 10,120 73.5
A number of the ditches on the Rio Grande have decrees with no priority, and are therefore not
included in the model. Table 3-29 lists the ditches, canals, decree, and appropriation dates for the decrees
with no priority that divert water from the Rio Grande.
87
Table 3-29. Irrigation Ditches and Canals Diverting Water from the Rio Grandein Water District 20 with No Priority Number
Irrigation Ditch Decree (Cfs) AppropriationDate
Centennial Ditch 164.80 11/01/1959Empire Canal 1,021.00 11/01/1959Farmers Union Canal 1,310.45 11/01/1959Monte Vista Canal 681.54 11/01/1959Prairie Ditch 734.04 11/01/1959Rio Grande Canal 2,208.00 11/01/1959Rio Grande Res./Santa Maria Res. Exchange 300.00 04/30/1981Rio Grande Res./Continental Res. Exchange 250.00 07/31/1983Tres Rios No. 1 6.50 12/31/1991Tres Rios No. 2 6.50 12/31/1991Tres Rios No. 3 0.85 12/31/1991Tres Rios No. 3 2.00 12/31/1991Tres Rios No. 4 1.50 12/31/1991Tres Rios No. 4 2.00 12/31/1991
When all decrees for reservoir storage are deleted from the data for Water District 20, 774 of the original
861 decrees remain. This data refinement leaves 380 of the original 454 irrigation ditches and canals
with a total of 7,415 cfs to address.
As shown in Table 3-30, after deleting diversions for reservoir storage and decrees with no
priority, the total amount of decrees in Water District 20 declines to 7,415 cfs. The Rio Grande accounts
for over 77% of the remaining decrees while the six largest ditches on the Rio Grande account for over
56% of all diversions in Water District 20. The Rio Grande’s proportion of Water District 20 water rights
declined because many of the water rights without a priority assignment represented Rio Grande
diversions.
Table 3-30. Total Decrees from Water District 20, RioGrande and Six Ditches with Largest Decrees afterDecrees with no Priority Number DeletedLocation Decrees (Cfs) % of WD 20Water District 20 7,415.183 100.0Rio Grande 5,729.260 77.3Top 6 Decrees 4,164.640 56.1
88
The six ditches diverting the largest amount of water account for over 72% of diversions from
the Rio Grande (Table 3-31). There is a considerable drop between the sixth largest ditch (by decree
amount) and the next largest, which is the Rio Grande Lariat Ditch with 106.8 cfs. This decree represents
less than a third of the San Luis Valley Canal, which is the sixth largest and is less than two percent of all
Rio Grande decrees.
Table 3-31. Six Irrigation Canals and Ditcheswith Largest Decrees in Water District 20After Deleting Decrees in Acre-feet and NoPriorityDitch Name Decree (Cfs)Rio Grande Canal 1,648.5Farmers Union Canal 801.45Empire Canal 505.92Prairie Ditch 500.98Monte Vista Canal 367.02San Luis Valley Canal 340.77
Not only is the amount of the decree critical in modeling producer response to a sustained
drought, so too is the priority of the right. A severe and sustained drought means that not all priorities
will be satisfied. The selection of irrigation ditches to include in the model is also based upon whether
the simulated ditches have senior rights that will continue to receive water during periods of low river
flow. The ditches that receive water during low river flows are determined by analyzing which ditches
received water during average historic Rio Grande flows.
Decrees on the Rio Grande, excluding those deleted because they represented reservoir rights or
were rights with no priority assignment, were ordered by the priority assigned by the Division of Water
Resources to determine which irrigation ditches and canals receive water when river flows are below
normal. These priorities are not sequential, so a new priority number was assigned that is sequential from
1-323. As shown in Table 3-32, of priorities higher than 75, the six largest irrigation ditches account for
only 3.3% of decrees. However, the 75 decrees with the highest priorities account for only 8% of all
89
water decreed from the Rio Grande. The top 100 priorities account for 1,038.2 cfs of river flow. When
the river flow is 1,038 cfs, the six largest ditches would account for 44.8% of all water diverted for
agricultural irrigation from the Rio Grande.
Table 3-32. Comparing Priority and Decree of the Six Ditches with the Most Decreesand all Other Ditches with the Percent of Total Flow Required to Satisfy all Decrees
PriorityDecree of
OthersDecree
of 6
All Others% of
RequiredFlow
Top Six% of
RequiredFlow
RequiredFlow
Priority <=25 111.44 3.00 97.4 2.6 114.4425< Priority <=50 91.34 0.00 98.5 1.5 205.7850< priority <=75 209.40 11.20 96.7 3.3 426.3875< priority <=100 161.18 450.60 55.2 44.8 1,038.16100< priority <=125 128.30 450.70 43.4 56.6 1,617.16125< priority <=150 150.64 277.90 41.7 58.3 2,045.70150< priority <=175 31.15 780.42 30.9 69.1 2,857.27175< priority <=200 79.30 422.85 28.7 71.3 3,359.42200< priority <=225 49.07 848.43 23.8 76.2 4,256.92225< priority <=250 44.48 287.47 23.0 77.0 4,588.87250< priority <=300 153.91 632.07 22.5 77.5 5,374.85Priority >300 354.41 0.00 27.3 72.7 5,729.26
The ten-year (1986-1995) daily average, minimum, and maximum monthly stream flow for the
critical agricultural irrigation months for the Rio Grande as measured at the Del Norte gauging station
are included in Table 3-33. These data indicate that, when river flows are average, the six ditches with
the largest decrees would divert most of the water in May, June and July. However, during the remaining
months, the decrees from all other ditches could divert the majority of the water from the Rio Grande.
River flows at the maximum levels allow the six largest ditches to divert most of the water in all months.
When flows are at minimum levels, however, the six ditches with the largest decrees would receive only
minimal water.
90
Table 3-33. Rio Grande Daily Average, Minimum and Maximum Flow for 1986-1995 at Del Norte During Critical Months for Agricultural IrrigationMonth Average Flow
(cfs)Minimum Flow
(cfs)Maximum Flow
(cfs)April 738.3 227.0 3,580.0May 2,547.4 561.0 6,920.0June 3,321.4 1,020.0 7,150.0July 1,488.2 260.0 6,120.0August 715.4 189.0 2,450.0September 530.2 207.0 1,240.0
All of the minimum river flows occurred in either 1990 or 1994. According to the priorities and
decrees listed in Table 3-32, the six ditches with the most decrees would receive very little water during
these years. However, from the data in Table 3-34, addressing actual diversions, the six ditches
accounted for 50.1% and 57.0% of all diversions from the Rio Grande during these low flow years.
While the data in Table 3-33 provide an indication of the amount of water decreed for diversion,
they provide no information on who actually is diverting water for irrigation. To gain a better
understanding of which ditches are receiving water with various river flow levels, the actual diversion
data are analyzed. Of the total diversions identified for Water District 20, the Rio Grande accounts for an
average of 93.4% over the nine years of data analyzed. The six ditches with the largest decrees account
for 63.8% of all Rio Grande diversions and 59.6% of all diversions in Water District 20.
Table 3-34 identifies total annual diversions for 1987-1995. During the lowest flow year, 1988,
these six ditches and canals accounted for over 57% of all water diverted from the Rio Grande. In years
with higher river flows, the six ditches account for most of the water diverted. In the year with the
highest river flow (excluding 1987 which appears to be an anomaly), the six ditches with the most
decrees accounted for over 72% of all water diverted from the Rio Grande.
91
Table 3-34. Actual Rio Grande Diversions for the Six Ditches and Canals with the MostDecreed Water, all Other Ditches and Rio Grande Flow for 1987-1995 Del Norte GaugingStation
YearDiversions of Six
Largest (cfs)Diversions of All other
Ditches (cfs)Rio Grande Flow
(cfs)1987 168,261 77,766 512,9141988 106,362 78,872 219,2401989 119,730 87,782 249,1021990 132,844 92,819 265,1651991 172,573 89,810 306,2561992 140,434 86,126 245,6011993 206,203 90,743 330,5331994 155,188 93,208 272,2791995 258,590 98,782 419,169
The results of this analysis indicate that the six ditches containing the most decrees adequately
represent water diverted for agricultural irrigation from the Rio Grande.
Eleven of the 35 ditches not included in the analysis hold priorities higher than 100 accounting
for more than 130 cfs in decrees (Table 3-32). Removing these decrees from the analysis allows the six
ditches with the most decrees to account for more of the water in a drought situation.
Water RightsFour of the six irrigation ditches and canals that account for most diversions from the Rio
Grande are within the Closed Basin portion of the SLV. Water diversions for the Rio Grande Canal,
Farmers Union Canal (now called the San Luis Valley Irrigation District), Prairie Ditch and the San Luis
Valley Canal are explicitly simulated in the model. The Empire Canal (now called Commonwealth) and
Monte Vista Canal are included in the "all other" category for which water diversions are accounted for
by the model, but crop production is not simulated. Diversions by all irrigation ditches or canals are
accounted for to ensure available water for ditches explicitly addressed in the model is accurate.
92
Defining Representative Agricultural Areas
Representative agricultural areas were derived based upon location of the irrigation ditches and
canals in relationship to soil characteristics, and locations of the underlying aquifers developed as a
proxy for the Unconfined Aquifer. The Director of the San Luis Valley Water Conservation District
provided a detailed map of the SLV that identified the areas serviced by each irrigation ditch and canal.
These locations were mapped into a spreadsheet according to the U.S. Bureau of Land Management
system of land subdivision (Quadrant, Township, Range and Section). The study area lies between
Townships 39 and 43 North within Ranges 7 and 12 East.
Forty-seven representative agricultural areas were initially identified. However, when nine years
of crop data were analyzed, no crops included in the model (alfalfa, barley and potatoes) were grown on
four of the farms. In addition, ten of the farms were located on acres that did not own rights to surface
water. Therefore, only 33 representative agricultural areas are simulated with two different soil types
(sandy loam and loamy sand) that withdraw groundwater from 9 separate aquifers and divert surface
water from five irrigation ditches or canals. Not all representative agricultural areas have access to
groundwater, but all receive a portion of the surface water available. The methods used to define the
acres of each crop, farm size, aquifers, soil characteristics, and allocation of surface and groundwater for
the representative agricultural areas are included in the following sections.
Defining Crop AcresTen years of cropping data by quarter-section were obtained from the USGS for the study area.
The data include the number of acres and location of each crop grown from 1983-1994. Spreadsheet
maps were generated documenting the location of the primary crop grown on each quarter-section to
gain an understanding where different crops are grown in the study area. By knowing the Township,
93
Range and Quarter-section of each crop, it can be mapped to the location of each representative farm so
that the exact number of acres of each crop grown during the ten years can be placed directly at the farm
location.
The primary crops for the region are alfalfa, barley and potatoes. The model simulates crop
production on 112,129 acres which include 16,124 acres of alfalfa, 51,451 acres of barley, and 44,554
acres of potatoes. These data represent the ten-year average production acres for each crop. Using the
average acres allocated to each crop over a historical period accounts for crop rotation sequences. For
example, barley and potatoes are generally grown on the same fields. A ten-year average accounts for the
proportion of acres allocated to each crop and accounts for crop rotations and changing cropping
patterns. Acreage allocated to each crop is constrained to the average maximum acres of the crop grown
during the ten years. That is, a representative farm is constrained in the model to producing no more
alfalfa than has been historically produced on the given acres of the farm.
The maximum size of each representative farm is the sum of the acres allocated to each crop.
Representative farm sizes range from 154 to 12,847 acres as identified in the input file Farm Acre.txt.
Defining AquifersThe Unconfined Aquifer represents the sole source of groundwater for agricultural production
within the study area. The depth to groundwater, depth to the bottom of the aquifer, and the dynamics of
return flows from irrigation activities presented complications when trying to model the single large
aquifer. The aquifer is simulated in the model by dividing the Unconfined Aquifer into nine separate
smaller aquifers with similar characteristics that were defined through three steps.
First, the blue clay layer, which separates the Unconfined from the Confined Aquifer, represents
the depth of the Unconfined Aquifer, which changes from north to south and west to east in the Closed
Basin. The depth to the blue clay layer for all parts of the Unconfined Aquifer by Township, Range and
94
Section were obtained from the Colorado Division of Water Resources and incorporated into a
spreadsheet. The standard deviation of the depth to the blue clay layer for all cells within a defined
aquifer ranged from 5 to 9.3 feet or about 8%. Depths to the blue clay ranged from 50 to 130 feet.
Second, the elevation of each Section (cell) within the study area was derived from topographic
maps of the region. Aquifers defined for the model were further divided by grouping areas of similar
elevations. The elevation of the study area ranges from 7,545 in the northeast to 7,760 feet in the west.
The standard deviations of the differences between elevations within an aquifer ranged from 5.6 to 8.9
feet.
Third, to prevent the height of the aquifer from being above the surface, the relative elevation of
the blue clay layer was determined by subtracting the depth to blue clay from the elevation at the surface.
Each aquifer was then defined by identifying those cells (Sections) with similar relative elevations of the
blue clay layer and height to the surface. In general, the aquifer locations cover areas from northwest to
southeast with surface areas that range from 4,480 to 65,920 acres.
Aquifer volume, representing the amount of water available for pumping, is addressed as a
parameter for the first time period in the GAMS model as V(o). Water available from the aquifer
changes during the cropping season. Withdrawals for irrigation, recharge from water placed in recharge
pits, and drainage from irrigation due to sprinkler inefficiencies, and non-consumptive use by crops
make the aquifer volume dynamic.
Defining Areas with Similar Soil CharacteristicsColorado County Soil Surveys for Alamosa, Conejos, Costilla, and Rio Grande were used to
identify the soil characteristics for the optimization model and for the crop growth simulation model
used to derive the crop coefficients. The study area consists of 44 different soil types that represent more
than 50% of the soil in a given section. Soil classifications for the primary soil in each section were
95
identified to determine if the area could be represented by a few soils. The soils generally range from
loamy sand to gravelly sandy loam. For the simulation model, soils were identified as either sandy or
loamy sand to account for the most likely differences between the actual soils found in the area. The soil
type associated with each representative farm, the ditch, and aquifer from which water is withdrawn are
included in the model. The specific soil characteristics are not included explicitly in the model. Crop
coefficients for each production function are determined by the soil type and assigned accordingly to
each representative farm.
Allocation of Surface Water to Representative Agricultural AreasDitch shares are used in the model to allocate water from irrigation ditches and canals to
representative agricultural areas. Ditch shares are distributed differently in the study area, depending
upon the irrigation ditch company. When the irrigation ditches were built, shares were distributed
equally to producers diverting water from the ditch so that all farms of the same size were entitled to the
same amount of water. Over time, ditch shares were sold or traded until today when shares are not owned
in proportion to the size of farm. For example, quarter sections on the Rio Grande Canal hold from 5-35
shares with each share receiving the same amount of water. The number of shares owned by each quarter
section within the model is not known.
The Farmer’s Union Canal (San Luis Valley Irrigation District) is unique because it issues each
farm on the ditch one share for each quarter-section of cropland, and water is then allocated equally to
each share holder. Farm share of each ditch was determined by running the model with water allocated
proportionate to farm size, then changing proportions until the historical cropping patterns for all farms
were simulated.
Surface water is not typically applied directly to fields for crop production within the study area.
Between 80-95% of the irrigated acreage in the study area use recharge pits where surface water is
96
diverted to a reservoir from which water is pumped to the center pivot for irrigation or drains directly
into the aquifer through infiltration. A small cost penalty that is higher than pumping costs is applied
within the GAMS model to prevent irrigation activities that apply surface water diverted from irrigation
ditches directly to the field. For simplicity, in this analysis all water applied to recharge pits adds to
available water in the aquifer for the farm associated with that aquifer. Representative agricultural areas
are constrained to pumping no more than their combined groundwater right and recharge amount that are
tracked separately throughout the simulation. Groundwater rights are separate and distinct from surface
water rights, so surface water used to recharge the aquifer may be pumped without infringing upon the
groundwater right.
Allocation of Groundwater to Representative Agricultural AreasGroundwater pumping is constrained by whether a farm owns a groundwater right, the pumping
capacity of the farm, and available groundwater. Data for groundwater rights for the study area were
obtained from the Colorado Division of Water Resources. Rights were correlated to the representative
agricultural areas through Township, Range, and Section as identified in the data. Groundwater rights are
defined in cfs, which were converted to acre-feet per month for inclusion in the model. Groundwater
rights for each of the 33 representative agricultural areas are identified in the model.
Pumping capacities for each representative farm were determined by estimating the potential
amount of water that could be applied to fields if center pivots were run continuously 24 hours/day for
the length of the growing season. The number of center pivots on each farm is a function of total farm
acres - one center pivot for each 130 acres of crop land.
The amount of groundwater in the aquifer may decline over time from decreased snow melt
infiltration and if return flows from irrigation and recharge pits are not sufficient to maintain the aquifer
at capacity. Representative agricultural areas are further restricted to pumping less than their aquifer
97
share, which is based upon the size of the farm. That is, the farm’s aquifer share is a function of the total
acres that are above the aquifer. Aquifer share, as defined for the input file for the model, is included in
the model.
The amount of applied water available for crop growth is determined by the irrigation efficiency
of the irrigation systems. Center pivots in the study area are of similar age and efficiency and are
therefore treated that way in the analysis. An efficiency rating of 0.80 is used for all systems in the
analysis as defined in the model.
Costs and ReturnsEnterprise budgets were developed from budgets and a custom rate survey generated by
Colorado State University (Dalsted et al. 1996), and locally available data. Crop budgets for each crop
analyzed are included in the model. The crop budget identifies variable and fixed costs of all pre-harvest,
harvest, and operating costs.
Description of Crop Growth Simulation ModelCoefficients for crop production functions were developed for the crops considered in the GAMS
model using the crop growth simulation model developed by Cardon (1990). The modified van
Genuchten-Hanks model combines a FORTRAN model developed by van Genuchten that simulates
transpiration and redistribution of water and the Hanks BASIC model that simulates
irrigation/infiltration. The model employs a daily time-step to simulate the relationships between water
and soil, water and plant growth, and yield and evapotranspiration (ET) to derive relative yield
parameters based upon water available for plant growth. It simultaneously simulates water movement
through the soil profile and water uptake by the plant through a series of equations from the two separate
models. Site specific input files were generated to reflect growing conditions in the study area. The
remaining paragraphs of this section describe the crop growth simulation model parameters used.
98
The crop growth simulation model requires data for the hydraulic properties of the simulation
site, specifically the water content, matric potential, and hydraulic conductivity. Water contents varied
from 0.02 to 0.50 cm3/cm3 in increments of .02, for both sandy loam and sandy soils, to calculate matric
potential and hydraulic conductivity. Matric potential is calculated using Equation 3.26.
H=He (/s)-b (3.26)
Where: H = matric potentialHe = air entry water potential constants, -15.98 for sandy
soils and -30.20 for sandy loam soils ( Rawls et. al. 1992) = soil water contents = soil water content at saturationb = constant parameter equal to 2.87 for sandy soils (Ghosh 1977) and 3.5
for sandy loam soils (Campbell 1974).
The unsaturated hydraulic conductivity is estimated using a single hydraulic content measurement and a
moisture retention function (Campbell 1974):
K = Ksat(/s)B (3.27)
Where: K = unsaturated hydraulic conductivityKsat = saturated hydraulic conductivity (468 cm/hr for sandy
soils and 62.16 cm/hr for sandy loam soils) (Rawls et. al. 1992) = soil water contents = soil water content at saturationB = parameter equal to 4.48 for sandy soils (Ghosh 1977) and
for sandy loam soils (Campbell 1974 ).
The data from these equations are included in input files to run the crop simulation model. Input
files were used that included irrigation, rainfall, matric potential, and hydraulic conductivity parameters.
To generate crop production functions the number of irrigation events was varied to simulate changing
water availability. Alfalfa was provided up to 21, potatoes 24, and barley 16 irrigation events during the
growing season with varying amounts of water. To limit the number of permutations required to generate
an adequate production function, pair-wise combinations of possible irrigation strategies were simulated
that required 2,047, 256, and 4,095 input files for each of the crops and for each soil type.
99
Planting, irrigation and rainfall dates for each of the crops simulated (alfalfa, barley, and
potatoes) are included in the model. Rainfall is incorporated into the model the day after irrigation occurs
because this is the standard practice for adding water to the simulation model and because rainfall in the
study area is minimal during the growing season. Irrigation generally begins on 15 April for all crops and
continues until just before harvest. Scheduling for irrigation events were derived from generally
available local knowledge, including expert opinion at the Colorado State University Cooperative
Extension at the San Luis Valley Research Center, and the consulting firm, Agro Engineering.
A second input file, Van.fmk, is in the FORTRAN portion of the model, which is generated
once. Included in this file are the crop coefficients, potential ET, rooting depth, osmotic salt potential,
and matric potential at which yield is reduced by half. The osmotic potential is not relevant for this
study, but is included in the input file. In the row above these columns are additional soil property
variables. The first variable, 468, represents the saturated hydraulic conductivity for sandy soils. Next is
the total porosity followed by the matric potential at the inflection point defined by Hutson and Cass
(1987), which is calculated as:
Hi = a(2b/(1+2b))b (3.28)
Where: Hi = pressure potential inflection point
a = air entry water potential (a constant equal to -15.98 cm for sandy soils and -30.20 for sandy loam soils) (Rawls et. al. 1992)
b = constant parameter equal to 2.87 for sandy soils (Ghosh 1977) and 3.5 for sandy loam soils (Campbell 1974).
Relative yield parameters for each crop are derived by taking the ratio of model generated ET to
potential ET (USDA) for the study area. Figures 3-6 � 3-11 provide the data points generated by the crop
simulation model for each combination of irrigation strategies. Figures 3-12 -- 3-17 show the production
functions resulting from fitting a line to the point of maximum relative yield for each irrigation
combination (no irrigation, one irrigation, two irrigations, and so on, with each irrigation at a different
time).
100
0.00
0.20
0.40
0.60
0.80
1.00
0 2 4 6 8 10 12
Number of Irrigations
Rel
ativ
e Y
ield
0
0.2
0.4
0.6
0.8
1
0 2 4 6 8 10 12
Number of Irrigations
Rel
ativ
e Y
ield
Agronomic Data Used for Economic Analysis of Drought, Agriculture, San Luis Valley, Colorado
Figure 3-6. Relative Yield from Crop Growth Simulation Model with Each Possible Irrigation Combination for Alfalfa on Sandy Soil
Figure 3-7. Relative Yield from Crop Growth Simulation Model with Each Possible IrrigationCombination for Alfalfa on Sandy Loam Soil
101
0
0.2
0.4
0.6
0.8
1
0 1 2 3 4 5 6 7 8 9
Number of Irrigations
Rel
ativ
e Y
ield
0
0.2
0.4
0.6
0.8
1
1.2
0 1 2 3 4 5 6 7 8 9
Number of Irrigations
Rel
ativ
e Y
ield
Figure 3-8. Relative Yield from Crop Growth Simulation Model with Each Possible Irrigation Combination for Barley on Sandy Soil
Figure 3-9. Relative Yield from Crop Growth Simulation Model with Each Possible IrrigationCombination for Barley on Sandy Loam Soil
102
0
0.2
0.4
0.6
0.8
1
0 2 4 6 8 10 12 14
Number of Irrigations
Rel
ativ
e Y
ield
0
0.2
0.4
0.6
0.8
1
0 2 4 6 8 10 12
Number of Irrigations
Rel
ativ
e Y
ield
Figure 3-10. Relative Yield from Crop Growth Simulation Model with Each Possible IrrigationCombination for Potatoes on Sandy Soil
Figure 3-11.Relative Yield from Crop Growth Simulation Model with Each Possible Irrigation Combination forPotatoes on Sandy Loam Soil
103
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0 5 10 15 20 25
Number of Irrigations
Rel
ativ
e Y
ield
Model
Regression
0
0.2
0.4
0.6
0.8
1
1.2
0 2 4 6 8 10 12 14 16
Number of Irrigations
Rel
ativ
e Y
ield
Model
Regression
Figure 3-12. Regression Results to Derive Crop Growth Coefficients for Alfalfa on Sandy Soil
Figure3-13. Regression Results to Derive Crop Growth Coefficients for Alfalfa on Sandy Loam Soil
104
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0 2 4 6 8 10 12
Number of Irrigations
Rel
ativ
e Y
ield
Model
Regression
0
0.2
0.4
0.6
0.8
1
1.2
0 2 4 6 8 10 12 14
Number of Irrigations
Rel
ativ
e Y
ield
Model
Regression
Figure 3-14. Regression Results to Derive Crop Growth Coefficients for Barley on Sandy Soil
Figure 3-15. Regression Results to Derive Crop Growth Coefficients for Barley on Sandy Loam Soil
105
0
0.2
0.4
0.6
0.8
1
1.2
0 2 4 6 8 10 12
Number of Irrigations
Rel
ativ
e Y
ield
Model
Regression
0
0.2
0.4
0.6
0.8
1
1.2
0 2 4 6 8 10 12 14
Number of Irrigations
Rel
ativ
e Y
ield
Model
Regression
Figure 3-16. Regression Results to Derive Crop Growth Coefficients for Potatoes on Sandy Soil
Figure 3-17. Regression Results to Derive Crop Growth Coefficients for Potatoes on Sandy Loam Soil
106
Economic Analysis of Farm Response to Drought in New Mexico and West Texas
SummaryThis section of the report describes estimation of economic impacts of drought on irrigated
agriculture for the Rio Grande Basin of New Mexico and West Texas. The analysis is based upon
identifying cropping practices under full water supply conditions and estimating how those practices
adapt to various degrees of drought severity. Agricultural prices, yields, and production costs are
incorporated for 9 classes of crops, using New Mexico State University cost and return farm enterprise
budgets, adapted to irrigated agriculture in the El Paso, Texas area, where complete Texas A&M farm
budgets were not available. A linear programming model is used to represent behavior of commercial
producers who maximize net returns. This farm behavior adjusts to 49 combinations of surface and
groundwater shortages induced by drought, ranging from 3 to 0 acre-feet per acre of each water source.
Results indicate that for Elephant Butte Irrigation District, New Mexico income-maximizing net
returns averaged $376 per acre with 82,680 acres planted under a full supply of surface and groundwater.
Under the most severe drought, average net returns per acre rose to $538 on 19,950 acres of remaining
pecan orchards produced from a deep aquifer. Returns from all remaining crops are zero. If additional
water could be found, its economic value per acre-foot is $30 for surface water and $0 for groundwater
when there is a full supply of both. In the face of increased drought severity, the value of additional
water continues increasing to a maximum of $155 for the first acre-foot for surface water and $112 for
the first acre-foot of groundwater when there is none of both.
Results for Middle Rio Grande Conservancy District, New Mexico showed income-maximizing
net returns averaged $156 per acre with 54,000 acres planted under a full supply of surface water. This
area has no significant groundwater development. Under the most extreme drought of zero available
surface water for a year, net returns fall to zero with no production occurring. If added water were
107
available, its economic value per acre-foot is about $2 per acre-foot for surface water when there is a full
supply. As drought becomes more severe, the value of added water continues increasing to a maximum
of $44 per acre-foot for surface water when there is zero supply.
For El Paso area agriculture, results showed income-maximizing net returns averaged $409 per
acre with 53,300 acres planted under a full supply of surface water. There is no significant groundwater
development in this area. Under the most severe drought of zero available surface water annually, net
returns fall to zero with no production occurring. If additional water were available, its economic value
per acre-foot is zero when there is a full supply. As drought severity increases, the value of added water
continues increasing to a maximum of $213 per acre-foot for surface water when there is zero supply.
AnalysisLinear programming is a widely used method to determine the use of land, water, labor, and
other resources and their associated net returns to a commercial farm. This method consists of expressing
the farm producer’s aim as a mathematical production program that aims to maximize net income. The
decision maker is presumed to take actions that maximize net farm returns subject to a series of resource
and marketing constraints. These constraints represent the farm’s limited access to land and water
resources and are typically written as linear equations.
A Prototype ExampleThe following prototype example shows the general structure of the farm management problem.
Suppose a commercial farm operator faces limited resources of land and irrigation water, including 500
acres of land and 20,000 acre-inches of water to use in the irrigation season, which amounts to 40 acre-
inches per acre. This example shows an amount of water slightly above a full allocation water year for
the Rio Grande Project, where the designed full allotment is 3 acre-feet per acre. For this example, the
operator is assumed to have three production choices: cotton, alfalfa, and lettuce. Each of these crops
108
requires a certain amount of land and water, and also produces a known amount of net returns per acre.
Suppose those values are as shown below in Table 3-35.
Table 3-35. Water and Land Use in a Hypothetical Western Irrigated Farm
Crop land use (acres) water use (ac-inches/acre) Net Returns/acre
cotton 1 36 $145
alfalfa 1 72 $220
lettuce 1 45 $450
Equations representing the economic decision environment for the producer are:
Maximize net income = 145 * Cotton + 220 * Alfalfa + 450*Lettuce (objective function)
in which the opportunity to increase net income is limited by the following three constraints on available
resources:
1.0* Cotton + 1.0* Alfalfa + 1.0* Lettuce � 500 (Land acreage constraint)
36 * Cotton + 72 * Alfalfa + 45 * Lettuce � 20,000 (water constraint)
Cotton, Alfalfa, Lettuce � 0 (Non-negativity constraints)
The three terms cotton, alfalfa, and lettuce are variables that represent decisions (decision
variables), for which the value of each variable is unknown before solving the problem. They represent
the number of acres of each crop that should be grown to maximize the producer’s net income. This
solution method is called linear programming because both the objective function and the constraints are
algebraically linear. That is, none of the unknown terms have complicated exponents or other nonlinear
terms. Because all terms are linear, there are many computer programs available to solve the problem.
109
The answer to the above farm management problem produces what is called an optimal solution.
This optimal solution includes four important pieces of information for analysis of institutions for coping
with drought in agriculture:
1. The maximum value of the objective function (in dollars)
2. The income-maximizing levels for each decision variable (# of acres)
3. The total amount of each resource used (land and water) including anything left over
4. The economic value (shadow price) of increasing the supply of each fully used resource
by one unit; resources not fully used have a shadow price of zero. The shadow price is
the economic value to the farm operator if one more unit of the scarce resource could be
made available for use.
The above water and farm management problem has the following optimal solution, summarized in
Table 3-36.
Table 3-36. Solution to Hypothetical Farm Management Problem
Item Value
Objective (net income) $200,000
Optimal Crop Mix (acres) CottonAlfalfaLettuce
0 acres0 acres
444 acres
Resource Use LandIrrigation Water
444 acres20,000 acre-inches
Economic value (shadow price) of one more unit ($/unit)
LandWater
$ 0.00$ 10.00
110
The income-maximizing plan for this example produce a net income of $200,000 with the crop
mix shown. Only lettuce is grown in this example because its ratio of net income to water used per acre
is the highest of the crops. The producer uses all available 20,000 acre-inches of water but only 444 acres
of the 500 acres of land available. The shadow price measures what the producer can afford to pay for
another unit of each resource. Water is fully used in the optimal solution, so the producer is willing to
pay up to $10 for another acre-inch if he could find it. This is because one additional acre-inch produces
$450 in net income divided by 45 acre-inches of added water per acre. Purchasing some from a neighbor
or drilling a well are two possible sources of additional water. The shadow price for land, however, is
zero dollars since not all existing 500 acres of land are used.
One can estimate the response of the producer, using linear programming, to a variety of
conditions, including that of drought defined by water shortages. Impacts of drought can be estimated by
solving the above numerous times with different quantities of water available, and observing the
response of the producer’s objective function, crop mix, and shadow prices as water supply is
progressively reduced from a full supply to nothing.
Simulating a worsening drought, the availability of water is reduced systematically and the
optimal response by the income-maximizing producer measured.
Extending this simple example, the general farm management problem can be stated as:
� decision variables are represented as Xi for any given ith crop up to n crops,
� net returns per acre as NRi for each ith crop,
� resource use aij for each ith crop and the j th resource, and
� resource availability availj for up to k resources.
111
Using this more general notation, the problem is written as:
Maximize objective = (3.29)NR Xi ii
n
=∑
1
subject to: for available supply of all resources j = 1, 2, ...a X availij ii
n
j=∑ ≤
1
for i = 1 ,2,...X i ≥ 0
In practice, resource constraints may be enforced as inequalities (� or �) as well as equalities (=)
depending on drought or other conditions facing farm producers.
New Mexico and West Texas AgricultureAgricultural practices in New Mexico and West Texas consist of numerous supplies of
resources, including both surface and groundwater constraints as well as other limiting resources such as
land, labor and capital, technology constraints such as crop varieties, and weather conditions that
influence crop yields such as temperature and rainfall. The three agricultural irrigation districts studied
for this analysis include Middle Rio Grande Conservancy District (MRGCD), New Mexico, Elephant
Butte Irrigation District (EBID), New Mexico, and El Paso Water Improvement District #1 (EPWID)
near El Paso, Texas.
Each of the several hundred producers for this study in the three irrigation districts face their
own resource constraints and preferences for crops and resources. Determining the unique conditions for
each producer is impractical, which prompts use of the typical farm producer to represent the group.
112
Acreage Limits Several parts of the previous simple model were expanded to more accurately show the regional
response of each irrigation district. The presence of three major kinds of crops in this area of the Rio
Grande Basin prompted the use of three land classes for the land constraints.
The first group, vegetable crops including lettuce, chiles, or onions, are often grown on contract.
Such prearranged price and acreage agreements between producers and agricultural product buyers often
results in a nearly constant amount of land devoted to those crops from one year to the next. Total
demand within a given region typically changes little. Profitability is often high for such crops due to
their specialty nature, but can vary widely if too many acres are planted within a region or the nation.
Prices received in the study region can vary greatly in this situation, and for this reason vegetables are
typically highly profitable but risky. When planting lettuce, for example producers may clear $600 per
acre one year and lose $400 the next.
Row crops such as cotton or grain sorghum are generally less profitable but have somewhat more
stable returns than the vegetables. In general such crops are not forward-contracted and acreage grown
varies substantially as national prices vary.
Pecans are a major crop in southern New Mexico and West Texas and their large establishment
costs prompted their inclusion as a separate land class. This crop is highly profitable and producers will
likely go to great lengths to protect their large investment in orchards under times of drought. Several
growers have drilled wells 500 feet deep or more to help insure dependable supplies of water for this
valuable investment in the case of severe and sustained drought.
For these reasons, three separate land classes, one each for row crops, vegetables, and pecans
were set up for the model. Total acreage within each land class were established based on historical
information over the period 1988-1997, taking into account possible double cropping on some acreages
as well.
113
Perennial crops such as alfalfa and improved pasture also require an establishment year in which
no production takes place. Only variable costs of establishment are incurred in that year, yet scarce land
is taken up by the establishment activity. Suppose that alfalfa fields take one year to establish and
produce a crop in the following 4 years. A constraint reflecting this establishment requirement could read
ALFEST = 0.25 * ALF (3.30)
where the variables are acres of alfalfa establishment and alfalfa, respectively. The constraint above
means that if anything more than zero alfalfa acres (ALF) enters the optimal income-maximizing
solution, then one quarter of its acreage amount must also be in the establishment activity. This equation
requires that one quarter of the optimal alfalfa acres enters the solution, even though it contributes no
positive return to the overall net income objective, other than to insure re-establishment of alfalfa acres
over time. Similar constraints apply for irrigated pasture. Pecan acreage was assumed to be constant
given the long useful life of those orchards and the uncertainty of when the next serious drought may
occur.
Accounting for RiskAnother component of the model developed involves the notion of accounting for risk through
the use of a concept known as flexibility constraints. Maximization of income in farm level linear
programming models often results in overspecialization, that is, the maximization of net income under
the conditions described might result in the model predicting that all available 500 acres should be
planted with lettuce. The riskiness of vegetable production as well as the nature of forward contracts
precludes the option of all acres being planted to one or more vegetables. Consequently, two sets of
constraints were designed to allow a range of proportions for which the vegetable and row crops could
vary.
114
The nature of these constraints is written as:
(3.31)VEG propveg TOTVEGACREkk∑ ≤ max *
The above equation means that maximum proportions of vegetable acres are based on historical
high and low proportions from area historical acreage. Note that many types of a given vegetable (i.e.,
sweet Spanish onions and midseason onions) can be included in order to make up the total amount of that
vegetable type.
An additional constraint elsewhere in the program sums the total vegetable acres resulting in a
known value of the term TOTVEGACRE, which is used by the equation above. Constraints similar to
those shown above were also enforced for the row crops in the model. Inclusion of such flexibility
constraints is often used in agricultural production models to add more realism to the model-predicted
crop mix. The highly profitable crops will generally enter the solution at their maximum proportion and
the less profitable crops at their lower bound proportion.
The situation becomes more complicated as resource availability of essential inputs such as
irrigation water falls due to drought. Area-wide response by agriculture to drought typically shows that
the more profitable crops per acre-foot of water, such as pecans and vegetables, stay in the solution,
while less profitable row crops per unit water falls. For the EBID example, the program’s structure in
which there are 3 land classes (pecans, vegetables, and row crops) deals with this fact.
Nevertheless, historically observed responses to previous droughts teach the lesson that the
proportions of more profitable crops within a class (i.e., vegetables or row crops) sometimes increase as
water supply conditions fall from full supply. As water supplies fall, producers can be expected to
change to the more profitable crops within a classification, and that they will grow less, and sometimes
none at all, of the less profitable crops within a class.
Accounting for Drought
115
For these reasons, a mechanism was added to the flexibility constraints described above which
allows the range of producer responses to drought to widen as water supplies fall. Using the example of
EBID, a full water supply is defined as 6 acre-feet/acre consisting in the model of 3 acre-feet of surface
and 3 acre-feet of groundwater, reflecting the design of the Rio Grande Project and pumping permits
established by the New Mexico State Engineer’s Office.
For a given drought situation, the percent decline from this baseline was calculated. This decline
was then applied to the midpoint of the historically observed high and low proportion for each crop. This
calculation produced a percentage that could be added to the upper bound and subtracted from the lower
bound proportion, thereby widening the flexibility constraints more and more as total water supplies
dwindle. The example below illustrates this procedure in Table 3-37.
Table 3-37. Sample methods and data, illustrated for onions, Elephant Butte Irrigation District,New Mexico
1. Historically max proportion of crop 0.3 Historically min proportion 0.1Midpoint of range (.1 + .3)/2 = .2
2. Surface water supply in given drought 2.0 ac ft/acGround water supply 1.0 ac ft/acTotal water supply 3.0 ac ft/acFull water supply 6 ac ft/acPercent change (1.0 - 3.0/6.0) = 50% decline from full supply
3. Percent widening to be added/subtracted from full water supply crop proportions = percent change calc. In step 2 * midpoint of range = 0.50 * 0.2 = 0.10
4. Modified upper bound proportion = original upper bound plus change = 0.3 + 0.10 = 0.40
Modified lower bound proportion = original lower bound minus change = 0.1 - 0.10 = 0.00
116
For the example above, the original bounds of (0.1 and 0.3) are allowed to expand to (0.00 and
0.40) for the reduced water supply scenario with only 3 acre-feet per acre of total available water.
Similar calculations were programmed for all water availability scenarios examined and the upper and
lower bound proportions were allowed to widen as a function of reduced total water availability. An
additional lower bound proportion of zero was also enforced.
One additional component was added to the flexibility constraints. In some cases the widening of
the upper bound proportion can result in an absolute amount of acres well above historically observed
highs for a crop. Such a situation makes little sense in a drought, so a second set of maximum acreage
constraints for given crops were added. The program user may specify a maximum increase above the
normal upper proportion for which the widening impact on proportions may apply. An example is be a
10% increase above the upper proportion. The program would then generate a second type of maximum
acreage constraint for each crop type similar to the following:
(3.32)VEG propveg BASEVEGACREkk∑ ≤ 11. * max *
In this case, BASEVEGACRE equals the normal total base vegetable acres. This constraint places a
maximum upper bound on VEGk that is only 10 percent above historical highs. The optimization model
will select the constraint most binding of this latter type of constraint and the maximum proportion
constraints described earlier.
Crop-Water Production TechnologiesSeveral crop-water production technologies were also incorporated. Farm producers can respond
in several ways in times of drought. Including several crop water production options that vary the mix of
surface water and groundwater producers use, reflects the range of drought response actions producers
face.
8Texas A&M crop budgets were not available for El Paso area agriculture.
117
These production technologies were included in two ways. The first consists of alternative
production options based on water availability as summarized below. NMSU farm cost and return
budgets for EBID (Doña Ana County), MRGCD (Socorro county), and EPWID#1 (adapted from Doña
Ana County8) were used to represent water use by crops for a full water supply condition, referred to as
the ‘base’ technology. Those budgets were adjusted to historical drought conditions to estimate water
use, yields, and costs for two other crop-water use technologies. These included a 50 percent surface
water 50 percent groundwater option, referred to as a ‘mixed’ technology, and as well as a 100 percent
groundwater option, referred to as the ‘all groundwater’ technology. In fact, there is unlikely to be much
groundwater pumping for either EPWID#1 or MRGCD according to their respective managers.
A fourth technology was also considered, namely crop production from a deep aquifer, which
would only be used after all surface water and shallow aquifer groundwater is gone under the most
severe drought. For this deep aquifer technology, yields, costs, and returns were calculated only for
pecans as they are presumed the only crop capable of economically supporting the increased well drilling
and deep aquifer pumping costs.
A second set of water conservation choices was also incorporated to allow producers the option
of reducing their surface water use. These were applied to Upland and Pima cotton as well as alfalfa.
Production options with reduced total water use, referred to as "water short" production options, were
devised for each of the base, mixed, and all groundwater technologies described above. For EBID, water
use was cut back from 36 to 24 acre-inches on both Pima and Upland cotton, with a corresponding
reduction from 60 to 42 acre-inches on alfalfa. Yields and costs were reduced accordingly. An outline of
the approach is shown in Table 3-38.
118
Table 3-38. Crop Water use Technologies, Elephant Butte Irrigation District, New Mexico
ProductionTechnology
Description Crops
Base NMSU cost and return farm budgets, typically based on 100 %surface water
all
Mix Surface and groundwater mix includes 50% surface and 50%groundwater. Higher costs and/or lower crop yields occur.
all
All groundwater 100% groundwater used for all crops. Higher costs and lower yieldsdue to increased groundwater salinity.
all
Deep aquifer Drilling of deep wells to maintain pecan production in extremedrought.
pecans
FindingsResults of the income maximizing model, are presented in Table 3-39 for the case of EBID.
Total economic returns, drought damages, net economic value per additional acre-foot of water (shadow
price), and total acres planted, are shown for 49 combinations of ground and surface water available,
reflecting various drought severity levels.
Similar kinds of results are shown in Table 3-40 and Table 3-41 for the remaining two districts,
MRGCD and EPWID#1. For MRGCD, water applied varies from 6 to 0 acre-feet for surface
water, with no significant groundwater. For EPWID#1 applications vary from 4 to 0 acre-feet,
again with no groundwater. The same variables are shown for these two districts as for EBID.
Table 3-39. Economic Damages from Selected Water Shortages, Elephant Butte Irrigation District, New Mexico
Water supply Economic Returns Drought Damages Water’s value Land
SurfaceWater
(ac-ft/acre)
Ground-water
(ac-ft/acre)
Netreturnsper acre
($/acre)
Total netreturns all
acres
($)
Economiclosses/acre:compared tofull supply
($/acre)
Total EconomicLosses all
acres:compared to
full waterallocation
($)
Added value + 1 a-f ($/ac-ft)
AcresPlanted
(acres)surface ground
3.0 3.0 375.97 31,085,082 0.00 0 30.12 0.00 82,680
2.5 3.0 359.44 29,718,155 16.53 1,366,927 30.12 0.00 82,680
2.0 3.0 335.87 27,769,403 40.10 3,315,679 43.92 0.00 82,680
1.5 3.0 311.79 25,778,949 64.18 5,306,133 43.92 0.00 82,680
1.0 3.0 287.72 23,788,495 88.25 7,296,587 43.92 0.00 82,680
0.5 3.0 263.64 21,798,040 112.33 9,287,042 43.92 0.00 82,680
0.0 3.0 239.57 19,807,586 136.40 11,277,496 43.92 0.00 82,680
3.0 2.5 375.97 31,085,082 0.00 0 30.12 0.00 82,680
2.5 2.5 359.44 29,718,155 16.53 1,366,927 30.12 0.00 82,680
2.0 2.5 335.87 27,769,403 40.10 3,315,679 43.92 0.00 82,680
1.5 2.5 311.79 25,778,949 64.18 5,306,133 43.92 0.00 82,680
1.0 2.5 287.72 23,788,495 88.25 7,296,587 43.92 0.00 82,680
0.5 2.5 263.64 21,798,040 112.33 9,287,042 43.92 0.00 82,680
0.0 2.5 239.57 19,807,586 136.40 11,277,496 43.92 0.00 82,680
119
Table 3-39 (cont.) Economic Damages from Selected Water Shortages, Elephant Butte Irrigation District, New Mexico
Water supply Economic Returns Drought Damages Water’s value Land
Surface Water
(ac-ft/acre)
Ground- water
(ac-ft/acre)
Net returns peracre
($/acre)
Total net returns allacres
($)
Economic losses/acre:compared to full
supply($/acre)
Total Economic Lossesall acres: compared tofull water allocation
($)
Added value + 1 a-f ($/ac-ft)
AcresPlanted
(acres)surface ground
3.0 2.0 375.97 31,085,082 0.00 0 30.12 0.00 82,680
2.5 2.0 359.44 29,718,155 16.53 1,366,927 30.12 0.00 82,680
2.0 2.0 335.87 27,769,403 40.10 3,315,679 43.92 0.00 82,680
1.5 2.0 311.79 25,778,949 64.18 5,306,133 43.92 0.00 82,680
1.0 2.0 287.72 23,788,495 88.25 7,296,587 43.92 0.00 82,680
0.5 2.0 263.64 21,798,040 112.33 9,287,042 43.92 0.00 82,680
0.0 2.0 265.06 18,514,392 110.91 12,570,690 74.52 30.60 69,849
3.0 1.5 375.97 31,085,082 0.00 0 30.12 0.00 82,680
2.5 1.5 359.44 29,718,155 16.53 1,366,927 30.12 0.00 82,680
2.0 1.5 335.87 27,769,403 40.10 3,315,679 43.92 0.00 82,680
1.5 1.5 311.79 25,778,949 64.18 5,306,133 43.92 0.00 82,680
1.0 1.5 287.72 23,788,495 88.25 7,296,587 43.92 0.00 82,680
0.5 1.5 293.56 20,504,846 82.41 10,580,236 74.52 30.60 69,849
0.0 1.5 305.33 17,128,508 70.64 13,956,574 74.52 30.60 56,099
120
Table 3-39 (cont.) Economic Damages from Selected Water Shortages, Elephant Butte Irrigation District, New Mexico
Water supply Economic Returns Drought Damages Water’s value Land
Surface Water
(ac-ft/acre)
Ground- water
(ac-ft/acre)
Net returns peracre
($/acre)
Total net returns allacres($)
Losses/acre:compared to full
supply ($/acre)
Total Losses all acres:compared to full supply
($)
Added value +1 a-f ($/a-f)
AcresPlanted
(acres)surface ground
3.0 1.0 375.97 31,085,082 0.00 0 30.12 0.00 82,680
2.5 1.0 359.44 29,718,155 16.53 1,366,927 30.12 0.00 82,680
2.0 1.0 335.87 27,769,403 40.10 3,315,679 43.92 0.00 82,680
1.5 1.0 311.79 25,778,949 64.18 5,306,133 43.92 0.00 82,680
1.0 1.0 322.05 22,495,301 53.92 8,589,781 74.52 30.60 69,849
0.5 1.0 340.81 19,118,962 35.16 11,966,120 74.52 30.60 56,099
0.0 1.0 375.97 31,085,082 0.00 0 30.12 0.00 82,680
3.0 0.5 359.44 29,718,155 16.53 1,366,927 30.12 0.00 82,680
2.5 0.5 335.87 27,769,403 40.10 3,315,679 43.92 0.00 82,680
2.0 0.5 350.55 24,485,755 25.42 6,599,327 74.52 30.60 69,849
1.5 0.5 376.29 21,109,417 -0.32 9,975,665 74.52 30.60 56,099
1.0 0.5 418.74 17,733,078 -42.77 13,352,004 74.52 30.60 42,349
0.5 0.5 458.43 13,747,857 -82.46 17,337,225 110.40 66.48 29,989
0.0 0.5 458.43 13,747,857 -82.46 17,337,225 110.40 66.48 29,989
121
Table 3-39 (cont.) Economic Damages from Selected Water Shortages, Elephant Butte Irrigation District, New Mexico
Water supply Economic Returns Drought Damages Water’s value Land
Surface Water
(ac-ft/acre)
Ground- water
(ac-ft/acre)
Net returns peracre
($/acre)
Total net returns allacres
($)
Economic losses/acre:compared to full
supply($/acre)
Total Economic Lossesall acres: compared to full
water allocation($)
Added value of one more acre-foot
AcresPlanted
(acres)surface ground
3.0 0.0 375.97 31,085,082 0.00 0 30.12 0.00 82,680
2.5 0.0 359.44 29,718,155 16.53 1,366,927 30.12 0.00 82,680
2.0 0.0 379.05 26,476,210 -3.08 4,608,872 74.52 30.60 69,849
1.5 0.0 411.77 23,099,871 -35.80 7,985,211 74.52 30.60 56,099
1.0 0.0 465.74 19,723,532 -89.77 11,361,550 74.52 30.60 42,349
0.5 0.0 524.80 15,738,312 -148.83 15,346,770 110.40 66.48 29,989
0.0 0.0 538.18 10,736,752 -162.21 20,348,330 155.76 111.84 19,950
122
Table 3-40. Economic Damages from Selected Water Shortages, Middle Rio Grande Conservancy District, New Mexico
Water supply Economic Returns Drought Damages Water’s value Land
Surface Water
(ac-ft/acre)
Groundwater
(ac-ft/acre)
Net returns per acre
($/acre)
Total net returns allacres($)
Losses/acre: comparedto full supply
($/acre)
Total losses all acres:compared to full supply
($)
Added value +1a-f
($/a-f)
AcresPlanted
(acres)
6.0 0.0 156.18 8,433,934 4.01 0 2.28 54,000
5.5 0.0 155.04 8,372,320 5.15 61,614 2.28 54,000
5.0 0.0 153.90 8,310,705 6.29 123,229 2.28 54,000
4.5 0.0 152.76 8,249,090 7.43 184,844 2.28 54,000
4.0 0.0 151.62 8,187,476 8.57 246,458 2.28 54,000
3.5 0.0 147.32 7,493,366 12.87 940,568 44.28 50,863
3.0 0.0 144.53 6,299,033 15.66 2,134,901 44.28 43,582
2.5 0.0 140.63 5,104,699 19.56 3,329,235 44.28 36,300
2.0 0.0 134.75 3,910,366 25.44 4,523,568 44.28 29,019
1.5 0.0 124.95 2,716,033 35.24 5,717,901 44.28 21,737
1.0 0.0 105.26 1,521,699 54.93 6,912,235 44.28 14,456
0.5 0.0 45.63 327,366 114.56 8,106,568 44.28 7,175
0.0 0.0 0.00 0 160.19 8,433,934 44.28 0
123
Table 3-41. Economic Damages from Selected Water Shortages, El Paso Area Irrigation, Texas
Water supply Economic Returns Drought Damages Water’s value Land
Surface Water
(ac-ft/acre)
Groundwater
(ac-ft/acre)
Net returns per acre
($/acre)
Total net returns allacres($)
Losses/acre: comparedto full supply
($/acre)
Total losses all acres:compared to full supply
($)
Added value +1a-f
($/a-f)
AcresPlanted
(acres)
4.0 0 409.03 21,812,956 0.00 0 0.00 53,328
3.5 0 409.03 21,812,956 0.00 0 0.00 53,328
3.0 0 408.96 20,775,756 0.07 1,037,200 0.00 50,801
2.5 0 428.43 17,885,502 -19.40 3,927,454 0.00 41,747
2.0 0 458.72 14,994,561 -49.69 6,818,395 132.12 32,688
1.5 0 512.24 12,103,620 -103.21 9,709,336 136.56 23,629
1.0 0 632.32 9,212,679 -223.29 12,600,277 140.88 14,570
0.5 0 825.41 5,365,165 -416.38 16,447,791 213.84 6,500
0.0 0 0.00 0 409.03 21,812,956 213.84 0
124
125
Economic Analysis of Recreation Response to Drought in the Rio Grande Basin
Summary A significant barrier to the design of drought-coping institutions in the Rio Grande Basin
historically has been a lack of reliable economic information about how recreational values change with
reservoir levels or total annual streamflow production, or institutional adjustments to either. This section
presents findings on economic values of water for reservoir-based recreation at six major Basin
reservoirs.
Monthly telephone survey data were collected on fishing and other water-based recreational
visitors by origin and destination in 1988 and 1989 for a study conducted for the New Mexico
Department of Game and Fish (Ward et. al. 1997). Because lake levels fluctuated widely during the
telephone sample period, it was possible to isolate water’s effects from price and other visit predictors.
An estimated regional travel cost model containing reservoir levels as a visit predictor provided
information to compute economic values of water in recreation. These findings are limited to use values
of visitors who travel to the reservoirs and do not reflect passive use values to people who value the
reservoirs but never visit them.
BackgroundMultiple-use management of reservoir systems occurs throughout the Rio Grande Basin and
elsewhere around the world. In the Rio Grande Basin, both single reservoir management programs and
larger comprehensive basin-wide plans include multiple-use management. Within a river basin, many
uses of water complement and compete with each other, especially during periods of severe drought.
These uses include irrigation, hydropower, water quality, flood control, municipal water supply,
streamflow regulation, fish and wildlife enhancement, and recreation.
126
While various congressional acts and state and regional policies emphasize the importance of
designing institutions to increase the total economic value of water, several barriers have historically
made it difficult to manage these systems for their highest net economic benefit. One barrier is the lack
of reliable economic information about system gains or losses produced by altered storage and release
patterns at a series of reservoirs. Even less information is available about how recreational values change
with reservoir levels. Throughout the Rio Grande Basin, much of the reduced water levels in the late
summer and early fall reduce the reservoirs’ values for many recreational activities including boating,
sailing, waterskiing, swimming, and fishing.
Information on recreation economic water values permits recreation to be traded off with flood
control, irrigation, fish and wildlife, and other water uses for which methods are more widely available to
estimate benefits. Without a method to estimate recreational values, water managers cannot
economically justify holding water for recreational purposes. The Rio Grande Basin contains several
alternative uses for water; any one use may affect others through any or all of the quantity, quality, time,
and location dimensions (Young and Haveman 1985, p. 479). For example, one reason for low water
levels in this basin is prolonged drought periods and/or high summer demands for water in irrigation.
Designing institutions that operate in the interest of society requires that increase in recreation benefits
from holding water at reservoirs be compared to the benefits produced by the added agricultural and
municipal uses of water.
There have been several studies about water’s recreational value. Boyle and others (1993) used
contingent valuation methods to estimate effects of changes in river flows in the Colorado River on
recreational boating benefits. Young and Gray (1972) estimated recreation values of $3 - 5 per acre-foot
of water. Creel and Loomis (1992) estimated that an acre-foot of water in San Joaquin Valley wetlands is
worth about $300 for waterfowl hunting, fishing, and wildlife viewing. Their travel cost model included
a variable for water flow levels into the wetlands. Ward (1987) also used travel cost analysis to estimate
127
values from $20 to $30 per acre-foot of water released into the Chama River in New Mexico for anglers
and rafters. Hansen and Hallam (1990) estimated marginal values of water as a recreational fishery
resource. Cordell and Bergstrom (1993) used contingent valuation methods to estimate the impact of lake
level fluctuations on recreation benefits for four North Carolina reservoirs.
Despite these studies, our literature search found little evidence about how recreational values of
water vary over a wide range of drought-coping institutions or reservoir management plans. Basin-wide
management plans center on the timing, location, and duration of reservoir drawdowns over several
reservoirs in the system. Evidence about recreational values gained and lost from institutional change or
reservoir drawdowns is especially important for managers. However, not only is evidence about these
incremental values scarce, but factors that influence the water’s recreational value have seldom been
examined. One such study was conducted by Ward and others (1996), using methods similar to the ones
developed for this drought study.
This section presents an analysis of water’s economic value for reservoir-based recreation at the
six major Basin reservoirs: Heron, El Vado, Abiquiu, Cochiti, Elephant Butte, and Caballo. An estimated
regional travel cost model provides information to compute economic values of selected drought-coping
institutions that would alter reservoir levels. During the 1988-1989 period in which telephone visitor use
data were collected, most of the study reservoirs experienced considerable water-level fluctuations due to
normal reservoir operations. Although this was a fairly wet period, reservoir fluctuations were rather
large due to agricultural demands, so it was possible to observe recreational use over a wide range of
reservoir levels.
These water fluctuations let us estimate a travel cost model (TCM) with enough variation in
water level to isolate water effects from price and visitor demographic effects. Moreover, water level
changes during the drought were pronounced enough to allow an estimation of incremental water values
over the complete range of the six major basin reservoir capacities and reservoir water levels.
128
Methods of AnalysisLake recreational benefit is an empirical function of reservoir surface area based on the principle
that a greater number of visitors are attracted to reservoirs with larger accessible areas and longer
shorelines.
Benefit equations for both lake and instream recreation are based on observing how visitor travel
expenditures to lakes change in the face of lake level changes. Benefits are measured as visitor
willingness to pay for the recreation experience, using the travel cost method, described in detail in Ward
and Beal (2000). Regression methods are used to write equations that summarize visitor benefits under a
wide range of reservoir levels. Similar methods were used to develop the New Mexico Game and Fish
Department’s RIOFISH model, completed in 1991 (Cole et al. 1987; Cole et al. 1990).
RIOFISH is a simulation of 132 reservoir, river, and stream fisheries in New Mexico used for
comprehensive planning of sport fishery management. The RIOFISH model is based in part on the
telephone monthly survey data described earlier that was collected in 1988-89. It estimates statewide
benefits based on a regional travel cost demand model. The model is a function of travel cost, travel
time, catch rates, stocking rates, and site characteristics, and examines the effects of changes specified by
the user in reservoir volume, stream discharge, or other management activities on angler use and angler
benefits (Cole et al. 1986, 1987, 1990; Ward et al. 1997). Changes in water reservoir volumes, stream
discharges, or other management decisions are translated into changes in the willingness of anglers to
pay for the increased quality of the fishing experience brought about by the management decision, based
on changes in consumer surplus. To derive the partial benefit functions for the basin optimization model
described in this paper, multiple RIOFISH simulations were run by varying streamflows and reservoir
volumes and holding all other variables constant.
129
VisitationVisitation at all six Rio Grande Basin reservoirs is expressed as separate mathematical equations
for each reservoir. Each equation expresses total annual visits, in thousands of visitor days, as these days
vary according to the reservoir’s average annual volume, measured in acre-feet. Reduced volume reduces
visitor days for each reservoirs as shown in the equation below:
Visits = �0 (Reservoir Volume) $1 (3.33)
In order to express a separate equation for each of the six reservoirs, each of the six has its own �0 and �1
, as shown in Table 3-42. Using the example of Heron Reservoir, this table shows that visits are affected
by reservoir volume, and is expressed as:
Annual Visits at Heron = 51.93 (Reservoir Volume) 0.27 (3.34)
which is interpreted as saying annual visitation at Heron Reservoir is 51.93 times that year’s average
reservoir volume raised to the power 0.27. If, for example, average annual volume at Heron is 200
(thousand) acre-feet, annual visits are predicted to be (51.93 x (200) raised to the 0.27 power)) = 217
(thousand) visits per year.
BenefitsBenefits at all six reservoirs are similarly expressed as mathematical equations. Greater annual
average volume, in acre-feet increases recreation benefits, measured in thousands of dollars per year. The
benefits equation is of the form:
Benefits = �0 (Reservoir Volume) 81 (3.35)
in which benefits are expressed in thousands of dollars per year and volume is again measured in
130
thousands of acre-feet per year. Using the numbers for Heron Reservoir in Table 3-42, applying Equation
3.20 results in the following predicted benefits:
Annual economic benefits at Heron = 1096.63 (Reservoir Volume) 0.32 (3.36)
This means that annual visitation at Heron Reservoir is 1096.63 times that year’s average
reservoir volume raised to the power 0.32 as shown in Table 3-42. If, for example, average annual
volume at Heron is 200 (thousand) acre-feet, annual visits are predicted to be (1096.63 x (200) raised to
the 0.32 power) = 5976 (thousand) dollars in benefits per year, which is $5,976,000. Similar values can
be calculated for any reservoir level desired.
Table 3-42. Recreational Use and Benefit, Rio Grande Basin Reservoirs
Reservoir Visits Predictor (1000s days/year) Benefits Predictor (1000s $/yr)
�0 �1 �0 �1
Heron 51.93 0.27 1,096.63 0.32
El Vado 8.93 0.47 78.26 0.60
Abiquiu 7.02 0.27 104.58 0.34
Cochiti 8.16 0.33 105.64 0.43
El Butte 16.78 0.41 172.43 0.51
Caballo 2.72 0.58 18.36 0.76
ConclusionsFor the range of the lake levels observed in the Rio Grande Basin, annual recreational values per
acre-foot of water vary widely, and depend on the reservoir’s average volume in a given year. Our
estimated values of reservoir water are comparable with values reported in previous work. They are a
plausible updating of Young and Gray's (1972) findings. However, they are generally lower than those
reported by Creel and Loomis (1992).
131
Findings in this section have important implications for water managers, legislators, and other
policymakers who wish to design better drought-coping institutions in which recreational values of water
are traded with those used by agriculture, power production, and cities. In droughts or in times when
demands for competing water uses are high, economically efficient basin management will draw down
reservoirs that have lowest incremental values for recreation, other things being equal. Reservoir
drawdowns produce the smallest losses in regional recreation benefits when reservoirs are isolated, large,
and have steep bank slopes.
By contrast, drawing down reservoirs with high recreational values per acre-foot impose
considerable economic losses to the region’s visitors; these reservoirs typically have few substitutes, are
located near population centers, or have shallow slopes at the waterline. In drought periods or times of
high water demand, maintaining high lake levels at these sites will increase regional economic
efficiency, other things being equal. In this way, trade-offs between recreation benefits and the benefits
of competing water users can be identified for water managers and other decision makers.
132
Economic Analysis of Hydropower Response to Drought in the Rio Grande Basin
OverviewHydropower facilities have been one of the Rio Grande Basin’s fastest growing renewable
energy technologies. Construction was completed in 1991 on the last of three large new hydropower
projects, which increases the basin’s hydroelectric generating capacity from 24.6 megawatts in 1987 to
78.4 megawatts in 1991. This represents a 219 percent increase. No new facilities have been constructed
in the Basin since 1991.
Construction of a 12-megawatt hydro unit at Abiquiu Dam on the Rio Chama was completed in
1991. The $27.4 million project initiated by Los Alamos joins two other large new hydropower projects
recently completed: (1) the 30-megawatt hydro system at Navajo Reservoir on the San Juan River,
completed by the City of Farmington at a cost of $30 million in 1988, and (2) the 8.8-megawatt hydro
system at El Vado Dam on the Rio Chama completed by Los Alamos County at a cost of $13 million in
1990. Considering that the total capacity of the region’s electrical generation facilities in 1987 was 5,132
megawatts, hydroelectric's share is small.
The movement of water flowing from a higher to a lower elevation has long been recognized for
its energy value. The capacity of this water to create energy is considerably reduced in drought periods,
where reservoirs typically experience large drawdowns to meet other demands, including irrigation,
municipal and industrial, recreation, and fish and wildlife. To the extent that drought-coping institutions
are able to maintain reservoir levels at reservoirs in the basin with generation facilities, economic
damages from hydropower production loss will be reduced.
Hydropower is derived by converting the potential energy of water to electrical energy, using a
hydraulic turbine connected to a generator. The energy potential from available resources in the Rio
Grande Basin makes hydropower one of the most significant renewable energy resources in the region.
133
AnalysisReservoir volume in any time period determines its surface elevation and surface area. Area,
elevation, and volume are physical relationships linked to each other by the unique topography of the
surrounding area. Tables that tie a reservoir’s area, elevation, and capacity are used to determine the
surface area and volume of reservoirs based on the elevation of its water. One area-capacity and one
elevation-capacity mathematical function for each reservoir needed to be approximated. Ordinary least
squares polynomial regression was used to estimate these functions. The percentage of explained
variance (R2) for estimates of all relationships was greater than 0.99.
The economic benefit of hydroelectricity is defined as the value of power generated compared to
the cost of competing resources. The price of power is a function of the demand for electricity during any
period of time. Power plants in the Rio Grande Basin, especially during severe and sustained drought,
will be operated as run-of-the river. That is, the operation of the power plants in this basin, is not
dispatchable; the utilities manager can not control releases to meet changes in peak demand.
Electricity can be produced only when managers from agencies that control the reservoirs release
water. Electric utilities in the Rio Grande Basin must forecast their requirements for electricity in any
period before the start of its fiscal year without control over releases. They typically are able to generate
power from alternate sources or purchase it on the market to meet its requirements. Since reservoir
releases for power generate electricity in excess of the utility's forecasted requirements, the value of
nondispatchable hydroelectricity is equal to the market price of nonfirm energy, presently $0.02 per kwh.
If the releases were timed to meet peak power demands, hydroelectric benefits in the Rio Grande Basin
would typically be about $0.05 per kwh.
Hydroelectric benefits are a function of the effective head, defined as the arithmetic mean of the
difference between reservoir surface elevation and the receiving stream channel elevation in the current
and the subsequent time periods, and the release. However the difference between inflows and releases
134
over time affects a reservoir’s head and its surface area, which influences future lake recreation benefits.
More generally, any given release in any time period affects the economic value of all uses. It affects
current instream flows, and current and future downstream volumes and surface areas. Table 3-43 below
shows rated capacity in kilowatts for each of the six basin reservoirs at which there are hydroelectric
facilities. More details are in Ward and Lynch (1996).
Table 3-43. Hydropower Capacity, Rio Grande Basin
Reservoir Stream Rated Capacity (KW)
Heron Willow Creek none
El Vado Rio Chama 8,800
Abiquiu Rio Chama 13,600
Cochiti Rio Grande none
Elephant Butte Rio Grande 27,945
Caballo Rio Grande none
Sources: New Mexico Energy Conservation and Management Division, with web address:http://www.emnrd.state.nm.us/ecmd/html/Programs/Renewables/hydropower.html
Mathematical DocumentationThis section documents the variables, parameters, and equations needed to measure the
economic benefits of hydroelectric power and the benefits of various drought-coping institutions for
dealing with water supply shortfalls.
135
Table 3-44. Indices for Hydropower Model
r Reservoirs: El Vado, Abiquiu, Elephant Butte
g Hydroelectric generators installed at the reservoir: #s 1 and 2
m Month of operation, beginning at the start of the water year (October)
Table 3-45. Parameters for Hydropower Model
a Converts streamflow cfs to million acre-feet per hour: 8.26 X 10 -8
y Hours per year: 8760
p Price of electricity per kwh = $0.02
w Weight per cubic foot water: 62.5 pounds
f Thermodynamic efficiency of power plant: estimated at 90%.
l Factor to convert foot-pounds to kilowatts: 737 foot - pounds / kw
c Operating capacity for generator: 110% of rated capacity
k Kilowatts produced per each cfs released: k = wf/l
Columns listed below for the r index are illustrated by application to El Vado and Abiquiu
Reservoirs respectively. Similar computations were made possible for the Elephant Butte
Reservoir.
�r Initial volume in million acre-feet for a representative water year (1990)
0.106 0.134
�r Maximum volume in million acre-feet
0.186 1.2
�r g Elevation of tailrace (stream channel)
6735 6040
�r g Rated capacity of generator g (kw)
8000----
68006800
�r Minimum useable water volume of reservoir r in maf
0.025 0.025
136
�m Inflow to El Vado (cfs)
µm Lower bound on outflow from Abiquiu Reservoir
m Number of hours in month m
m r Streamflow into El Vado Reservoir in month m
�r g m Maximum amount of electricity that can be produced at reservoir r, by generator g, in monthm
�rgm = �rg c m
Hydroelectricity production depends on reservoir surface elevation. Using the area-
capacity-elevation data for the El Vado and Abiquiu reservoirs, 1st through 6th power polynomial
functions were estimated to relate elevation to volume. The intercept and parameters are listed
below for each of the two illustrative reservoirs, with applicable t-statistics in parentheses in Table
3-46.
Table 3-46. Area Capacity Relations
�0 r 6.77 x 10 3
(9842.285)6.16 x 10 3
(18153.795)
�1 r 3.44 x 10 3
(21.586)4.21 x 10 2
(89.373)
�2 r -9.21 x 10 4
(-9.932)-6.57 x 10 2
(-28.855)
�3 r 1.54 x 10 6
(7.274)8.22 x 10 2
(16.251)
�4 r -1.34 x 10 7
(-6.013)-6.20 x 10 2
(-11.138)
�5 r 5. 76 x 10 7
(5.238)2.49 x 10 2
(8.453)
�6 r -9.58 x 10 7
(-4.698)-4.08 x 10 1
(-6.847)
137
BKrgm� pKrgm (3.37)
Krgm
� Ergm
Rrgm
km (3.38)
Variables used for the hydropower model are shown in Table 3-47.
Table 3-47. Variables for Hydropower Model
Vr m Volume of reservoir r in month m (maf)
Sr m Surface area of reservoir r in month m (acres)
Rr g m Release from reservoir r that produces electricity in month m (cfs)
BKr g m Economic benefits of hydroelectricity produced at reservoir r, by generator g, in month m($/month)
Kr g m Quantity of electricity produced at reservoir r, by generator g, in month m (kwh)
Fr m Streamflow into reservoir r in month m (cfs)
Hr g m Head in reservoir r, at generator g, in month m (ft)
Er g m Effective head in reservoir r, at generator g, in month m (ft)
Wr Flow out of reservoir r not used to generate electricity (cfs)
EquationsThe economic benefit of hydropower is the price of the power times the amount of power
produced:
Power production is a function of the effective head; the flow released through the generators; a
constant (k) based on the weight of water (w), the efficiency of the generator (f), and the number of foot-
pounds per kilowatt (l); and the hours the generator runs:
The quantity of electricity produced is a function of the effective head and the release; but the
head is a function of the volume, which is a function of the release. To minimize the effect of large
138
Ergm
�Hrgm
� Hrgm%1
2(3.39)
Hrgm
� �0r � �1rVrm� �2rV2rm
� �3rV3rm
� �4rV4rm
� �5rV5rm
� �6rV6rm
� �rg
(3.40)
Vrm
� Vr(m&1) � (F
r(m&1) � Wr(m&1)� �
gRrg(m&1) )a(m&1) (3.41)
releases on the change in the head, the effective head is defined as the average of the heads in periods m
and m+1.
The head is the elevation of the water surface minus the elevation of the tailrace:
Reservoir volume is based on a simple mass-balance equation:
The volume in month m is the volume in the previous month plus the inflows minus the
outflows, the release through the generators and the flow that does not produce electricity. For this study,
benefits of hydropower production are computed on an annual time step, which means that total monthly
benefits are summed over the 12-month year.
Application to Drought StudyThe simple economics and hydrology model of basin hydropower provides a sound basis for
evaluating impacts of drought coping policies on hydropower benefits. Still, it was not possible to get the
hydropower benefits equation into the final model satisfactorily. Issues dealing with the law of the river
occupied most of our time, and hydropower appeared a small contributor to the Basin’s economy.
139
Economic Analysis of M&I Response to Drought in the Rio Grande Basin
SummaryThe use of water produces considerable economic value in a modern household. Besides
cooking, washing, cleaning, and sanitation, the typical American household uses water to maintain a
domestic environment in landscapes and lawns. While not all these uses of water are essential for
survival, they are still desired. Beyond the basic human requirements it satisfy water it has been
extensively analyzed as an economic resource for which there is a considerable urban demand,
particularly in the desert southwest. The willingness of people to pay for and use water in every day
activities is what gives water an economic value. Similarly, water shortages resulting from drought or
other interruption of services cause economic damages, for which people are willing to pay considerable
amounts to avoid. One overriding purpose of this study is to analyze the potential of innovative
institutional adjustments for coping with severe and sustained drought to reduce the size of those
economic damages.
AnalysisThe economic value of water to the residential household is based on the idea of demand. People
express this demand as a quantity of water they choose to use at various possible prices. For all
household uses except the most basic essential purposes, quantity of water used is reduced in the face of
higher prices and it increases as the price falls. The scarcity of water increases considerably as a drought
becomes more extreme.
Significance of Municipal UsesWater is essential to life, and municipal suppliers provide this water. People can survive only a
matter of a few days without water. Nevertheless, the daily per capita requirement of drinkable water
140
necessary for survival is so small that water is no longer priceless after a few quarts have been made
available. Daily per capita domestic water use in the Rio Grande Basin and elsewhere in industrialized
countries is many times that the level of consumption required for survival. The quantity actually used
for municipal use, depends on consumption patterns and habits as well as relative availability and cost of
water. A wide range of per capita rates of consumption is possible.
Special Problems of Municipal Water ValuationThe value of municipal water is defined by consumers’ demand for it, and is measured by the
amount consumers would be willing to pay for it. Consumption of municipal water is influenced by
price, consumer income, population, by the configuration of commercial and civic uses of water, and by
climate, especially rainfall during the season when home landscapes need water.
Most evidence indicates that water consumption is not greatly responsive to either price or
income, at least within the range of observed variability. This can be explained by the fact of the small
proportion of expenditures on water of total national consumption expenditures. This means that price
could increase significantly and water consumption would only be reduced slightly.
However, water consumption studies have shown that users do respond some to changes in price.
Where water is metered, consumers have been found to use significantly less water than those who are on
a flat rate. In cases when water is not metered, consumers pay a price of zero for additional water use.
By contrast, metering means consumers pay a price for additional use larger than zero. Lawn and other
outdoor landscape use of water is particularly sensitive to price changes.
Water pricing policies in many cities is complex enough so that it is difficult to infer much about
consumers’ willingness-to-pay, since they are not able to consume all they want at a constant price.
Where water is sold on a flat-rate basis, the marginal price to the consumer is effectively zero. A number
9Price elasticity of demand is defined as the percentage change in quantity of a commodity consumed givena 1 per cent change in price. The sign on the elasticity coefficient is generally negative. The coefficient provides aconvenient way of summarizing the price responsiveness of demand.
10Young and Gray (1972) emphasize that in assessing the value of municipal water, it is not the value of rawwater that is reflected by the demand curve for residential water, but the value of treated water which has been giventhe added attributes of time and place utility. Because treated water delivered to peoples’ homes have been given thisutility, the costs of treatment, storage, and distribution must be subtracted from the higher values above to derive valuesof raw water in watercourses, which will be comparable with values derived in other uses for raw water.
141
of published studies of the price elasticity of demand for municipal water 9 are available. Price elasticities
tend to be relatively low, and differ between the two major components of use, domestic (indoor) use and
outdoor use, such as lawn watering. The elasticities also vary among the different regions of the country.
Demand functions for water are the place to start when measuring people’s willingness-to-pay
for municipal water. Because the demand for indoor and outdoor uses typically respond to different
factors and meet different needs, these two demands are best considered as two separate schedules. The
willingness-to-pay concept can be applied to both uses.10
If one can derive a relationship on the amount of water people use at different water prices (a
demand schedule) from observations of water use in the face of varying prices, this relationship can be
used to estimate the total benefits of water as a mathematical function of supply. The same relationship
can be used to estimate economic damages associated with water supply shortages caused by drought.
Seven study areas were selected for that study, and with the cooperation of water utilities in three
southwestern states, information on residential water use, rate structures, revenues from water sold and
non-price conservation programs covering the period from 1980 through mid-1995 was collected. The
study area cities are: Los Angeles and San Diego, California; Broomfield and Denver, Colorado; and
Albuquerque, Las Cruces and Santa Fe, New Mexico. Similarities and differences in residential water
use, prices and rate structures, climatic conditions and demographic characteristics of people who live in
the study areas
142
provide an excellent cross-section of factual data for cities in the southwestern United States. These cities
also exhibit a wide range of non-price conservation programs, from cities that have numerous ongoing
water conservation programs to cities that have yet to implement any at all.
FindingsThe general findings of this study show that water price has a significant and negative impact on
water use. However, despite the significance of price in influencing use, water demand is insensitive to
price changes alone. Economists sometimes express this by saying water demand is very price inelastic,
which means that large percentage increases in price are required to induce small percentage decreases in
water use. The price elasticity of demand for water is measured as the percentage reduction in use from a
one percent increase in price. The highest price elasticity estimate was for summer use (approximately -
0.20). At this degree of consumer responsiveness, water utilities could double their water rates (increase
them by 100 percent) and expect only a 20 percent decrease in water use during the peak season.
Similarly, if a drought reduced supplies by 20 percent, demands would exceed supply unless prices
increased by 100 percent. Overall, water utilities in the region can expect a water price elasticity of -0.10
on an annual basis; a 100 percent increase in rates will reduce use by 10 percent.
Nonprice conservation programs appear to be most effective only after a water utility achieves a
critical mass of conservation programs. For Los Angeles, San Diego and Denver, the large number of
non-price programs have had the desired effect of reducing demands. For cities with fewer programs or
relatively new experience with conservation programs, non-price programs show no observable effect on
reducing demand. Conservation programs appear to work independently of a drought environment, such
as California’s severe drought in the late 1980s and early 1990s. Their conservation programs have
continued to work after the drought conditions have ceased. Conservation programs may be ultimately
143
necessary simply to counteract increases in residential use of water brought about by factors outside the
control of water utilities, such as population growth and increased demands for swimming pools and
lawns.
Climate effects residential use in predictable ways. Water use is strongly influenced by average
monthly temperature and seasonal changes in temperature. However, surprisingly, precipitation was
consistently found to be an insignificantly factor in affecting use, in all analyses performed. All cities in
this analysis are semi-arid to arid in climate, so the ratio of water use by plants (evapotranspiration) to
precipitation is much greater than one. Landscape watering is necessary to maintain residential lawns and
trees. Random and infrequent rains do not change residential watering patterns to a significant degree.
Other factors, beyond the control of a water utility, such as residential income and city population, also
vary but their influence is estimated to have a relative minor impact on per capita residential use.
In summary, both price and non-price conservation programs are effective, but require a major
commitment to implement. Consumers are unresponsive to price increases under current typical rate
structures, requiring large increases in price to achieve small reductions in demand. Nonprice
conservation programs appear to be most effective when there are a substantial number of programs
conducted over longer periods of time. Because information regarding nonprice programs is incomplete,
we are unable to distinguish the effectiveness of individual types or specific programs nor the residual or
lasting effects of nonprice programs. Small changes in water rates or implementation of haphazard
conservation programs will most likely not produce discernable results in reducing per capita water use.
We use the empirical demand schedule findings over all these cities from the Michelson study by
applying the results to the climatic and demographic conditions of Albuquerque and El Paso. The
demand model is remarkably good in predicting water use in the two cities. For example, predicted
144
residential monthly consumption was computed for actual use in El Paso for 1988 - 1996. This is an out-
of-sample comparison. With the El Paso water price structure, the model estimates that residential
demand has a -0.115 demand elasticity.
Tables 3-48 and 3-49 show the application of the estimated demand functions for Albuquerque
and El Paso. Formulas used for total benefits of added water as a function of water use are shown in the
table footnotes. The functions are used to predict the market-clearing prices of water (price that reduces
shortages to zero) if residential water is curtailed by various percentages due to drought. To illustrate use
of the formulas, we show the impacts of percentage reductions from current (1998) usage of 5%, 10%,
15%, and 20% due to various severity of drought.
Drought DamagesAs water use is cut back due to drought, the market-clearing price increases considerably due to
the very low price elasticity of demand. Another way of stating this finding is that water users are willing
to pay a higher price per unit in the face of more severe shortages. In Albuquerque, for example, the
market-clearing price for water increases from $1.29 to $4.12 per 1000 g per month. The average of the
with and without-drought market clearing price times the amount of curtailment is a good estimate of the
economic loss produced by the drought.
Continuing with the Albuquerque example, consider the curtailment due to drought from 14.7 to
13.4 thousand gallons per month per household. This curtailment produces a $3.52 economic loss for the
household. The loss is computed as (14.7 � 13.4) x ($1.29 + $4.12)/2 = $3.52. Note the initial and final
market-clearing prices are averaged. The total loss for the city due to this water supply curtailment on an
annual basis is estimated $ 376,640. This loss is computed as $3.52 x 107,000 = $376,640, based on 1998
actual water use levels.
145
Table 3-48. Economic losses for selected water use curtailments due to drought: AlbuquerqueFull
SupplyCurtailment Percentage
5% 10% 15% 20%
Number of households (numbers) 107,000 107,000 107,000 107,000 107,000Total Use (acre-feet per / year) 100,000 95,000 90,000 85,000 80,000
Residential 58,000 53,000 48,000 43,000 38,000Other 42,000 42,000 42,000 42,000 42,000
Residential Use (1000 gal / mo) 14.7 13.4 12.2 10.9 9.6Price ($ / 1000 gal) 1.29 4.12 6.73 9.56 12.39
Slope: increase in price ($/1000gal) per unit increase in water use(1000 gal / mo).
- 2.18
Intercept: Price at which utility-supplied water use per householdfalls to zero
33.29
Formula used for demand: linearfunction of use, Figure 3.7a
Price = Intercept + Slope * Use = 33.29 - 2.18 * Use
Formula for total benefits ofwater use: quadratic function ofuse, Figure 3.7b
Total benefits = Intercept * Use + 0.5 * [ Slope * Use 2 ] = 33.29 * Use - 0.5 * [ 2.18 * Use 2 ]
146
Table 3-49. Economic losses for selected water use curtailments due to drought: El PasoFull
SupplyCurtailment Percentage
5% 10% 15% 20%
Number of households 120,553 120,553 120,553 120,553 120,553Total (1998) Use (acre-feet/year) 107,000 101,650 101,650 101,650 101,650
Residential 58,850 53,500 53,500 53,500 53,500Other 48,150 48,150 48,150 48,150 48,150
Residential Use (1000 gal/mo) 13.3 12.0 10.7 9.4 8.1Price ( $ / 1000 gallons) 0.94 3.70 6.46 9.22 11.98
Slope: increase in price ($/1000 gal) perunit increase in water use (1000 gal /mo).
- 2.12
Intercept: Price at which utility-supplied water use per household falls tozero
29.18
Formula used for demand: linearfunction of use, Figure 3.7c
Price = Intercept + Slope * Use = 29.18 - 2.12 * Use
Formula for total benefits of wateruse: quadratic function of use, Figure3.7d
Total benefits = Intercept * Use + 0.5 * [ Slope * Use 2 ] = 29.18 * Use - 0.5 * [ 2.12 * Use 2 ]
147
Figure 3-18a. Residential Demand for Water Per Household, Albuquerque
0
5
10
15
20
25
30
35
0 2 4 6 8 10 12 14 16
1000 gallons/month
Pri
ce (
$/10
00 g
allo
ns)
Historical price and use, 1998
Price and use, 5% supply
Figure 3-18b. Economic Value of a Range of Water Uses-Per Household, Albuquerque
0
50
100
150
200
250
300
0 2 4 6 8 10 12 14 16
1000 gallons/month
Ben
efit
s ($
/ho
use
ho
ld/m
on
th)
Benefits from historical use, 1998
Benefits with 5% supply curtailment due to drought
148
Figure 3-18c. Residential Demand for Water Per Household, El Paso
0
5
10
15
20
25
30
35
0 2 4 6 8 10 12 14
1000 gallons/month
Pri
ce (
$/10
00 g
allo
ns)
Historical price and use, 1998
Price and use, 5% supply curtailment
Figure 3-18d. Economic Value of a Range of Water UsesPer Household, El Paso
0
50
100
150
200
250
0 2 4 6 8 10 12 14
1000 gallons/month
Ben
efit
s ($
/ho
use
ho
ld/m
on
th)
Benefits with 5% supplycurtailment due to
Benefits from historical use, 1998
149
System Operation under Law of the River
OverviewRio Grande water resources are allocated under a complex set of institutions. These include the
Rio Grande Compact, federal laws, court decisions, administrative rules, and a treaty between the United
States and Mexico, which are described collectively as the "Law of the River." The Law of the River
determines the water allocations under which use of Basin water resources are made. The method for
characterizing the Law of the River for allocating future water shortages in periods of drought is
described below. For each drought scenario considered, the current Law of the River is described, which
is the baseline institution for allocating water, and for which a forecast is made of the resulting water use
patterns. Compared to that baseline, a forecast is made for water use patterns and changes in economic
benefits under all other institutional options considered. The difference in water use patterns and
economic benefits between the Law of the River and each other institutional option for coping with
drought are presented to show the relative effectiveness of each institutional option considered. How the
Law of the River was modeled for allocating flows in the Basin also is described in this section.
Rio Grande CompactThe Rio Grande Compact is the overriding mechanism for allocating water under the Law of the
River. The following section describes implementation of the model to reflect the way it is written in the
Compact. The discussion captures the essence of how the model allocates water under the Compact.
Water Colorado delivers to New Mexico at the Lobatos gage is a function of headwater flows in
Colorado. These headwater flows, called Index flows for the Rio Grande Compact include three Conejos
River Index gages plus the Rio Grande gage near Del Norte. Any water not delivered to New Mexico is
11The authors are indebted to Mr. Wayne Treers, US Bureau of Reclamation, El Paso, Texas for explainingthe complexities of Reclamation’s operation of the Rio Grande Project.
12We refer to this system in the remainder of this report as Elephant Butte only. However the Bureau ofReclamation manages the two reservoirs as a single system.
150
available for use by Colorado. Equations are written in the model to summarize annual flows at the
Lobatos gage, and therefore water available for use by Colorado, as a function of the Index flows
described above.
Water New Mexico delivers to Texas at Elephant Butte, and measured at the gaging station
below Elephant Butte, is a function of annual flows at the Otowi gage, not including San Juan Chama
flows, which are available for use entirely in New Mexico. Equations are used in the model to deliver
water to the Elephant Butte gage based on native flows at the Otowi gage (total flows minus imported
San Juan Chama flows).
In very wet years, when New Mexico does not have the capacity to use its full Compact
allocation, New Mexico may receive an annual credit of up to 200,000 acre-feet for its overdelivery to
Texas. In dry years, New Mexico may underdeliver to Texas by an amount not to exceed 150,000 acre-
feet, and an annual debit is incurred in such cases. New Mexico, under the Compact, may accrue total
debits, offset by wet year credits, of up to a total of 200,000 acre-feet. Accrued debits and credits are
subject to system losses, including evaporation that would have occurred had the debit or credit not been
incurred. No attempt is made to calculate such losses precisely, but they are estimated at 15% annually.
Water Allocation Below Elephant Butte Reservoir11 The Compact does not apportion the water released from Elephant Butte-Caballo Reservoir
system12 between New Mexico and Texas. Historical contracts between the irrigation districts in the two
states and the Bureau of Reclamation resulted in a constant ratio of irrigated land of approximately 57%
in New Mexico and 43% in Texas, described more fully below. Based on this historical ratio, and the
13While the 1906 Treaty states that Mexico will receive 60,000 acre-feet annually, they have not received thefull 60,000 acre-feet in drought conditions. Article 2 of the Treaty states that Mexico will receive its amount of waterin the same proportion as the water supplied to the lands within the Rio Grande Project (U. S. irrigated lands). Since1951, IBWC and the Bureau of Reclamation have agreed on the Rio Grande Project allocation procedure such thatMexico will share in the same shortage as the U. S. irrigation districts. When total Project storage falls belowapproximately 1,000,000 acre-feet by Dec. 1 in any year, then less than full supply allocations are issued to the Districtsand Mexico, and the allocations can be increased if subsequent inflow to Elephant Butte/Caballo reservoirs increasesduring the irrigation season. The authors are indebted to Wayne Treer for this insight.
151
Bureau’s "DII" operating rule, the model allocates diversions from Project releases (after accounting for
conveyance losses and the delivery to Mexico) in the ratio of approximately 57% to New Mexico and
43% to Texas. The New Mexico allocation goes entirely to irrigated agriculture, while the Texas
allocation is proportionally distributed between City of El Paso M&I use and use by Texas irrigated
agriculture. This proportional allocation occurs in the model, because the Texas water allocation goes to
El Paso County Water Improvement District #1, and the City of El Paso is a contractor like any other
farmer in the District.
Water Delivery to MexicoBased on the U.S. Mexico Treaty of 1906, 60,000 acre-feet of water per year is allocated to
Mexico by the model.13 For model simplicity, and because of the potential issues raised with any future
delivery reductions to Mexico (despite such provisions under "extraordinary drought" in the Treaty), a
constant 60,000 acre-feet annual delivery is assumed.
Summary of MechanicsThis outline summarizes the model’s forecast water use patterns under the Law of the River for
three areas: water allocations below Elephant Butte Reservoir, water allocations within New Mexico
above Elephant Butte, and water allocations in Colorado.
14The Bureau of Reclamation has a method for calculating the yearly allocation to the U. S. Districts and toMexico. It first looks at existing total storage in both reservoirs on December 1 each year. Then the total storage figureis adjusted for: estimated evaporation losses for both reservoirs for an entire irrigation season; Rio Grande Compactcredit waters existing in Project storage; and, any non-Project water (such as San Juan-Chama water) existing in Projectstorage. These adjustments are subtracted from the total storage amount, and the net figure is the amount of storageallotted toward the yearly allocation at the diversion headings. If the net storage amount is less than 790,000 acre-feet,then a less-than-full supply allocation is given to the U. S. Districts and Mexico based on the historic ratio of irrigatedlands of the U. S. Districts and Mexico’s delivery to the Acequia Madre heading and the release from Project storage.
152
Below Elephant Butte ReservoirStorage-Release Rules for Elephant Butte. A full release from Project storage (water stored at Elephant
Butte and Caballo) is defined as 790,000 acre-feet. However in drought periods, as Project storage falls
below 1 million acre-feet, the water districts have historically released much less than the 790,000,
holding water project storage as a savings account for the future. An examination of annual Project
releases over the last 20 years was performed. Results of several regression analyses showed that Project
releases were higher in years when Project storage was higher, and lower in years with lower levels of
tributary inflows into Project storage. The historical relationship of best fit between Project releases,
Project storage, and tributary inflows into Project storage of best fit was found to be: Project release =
672,000 + (0.14 * Project storage) - (1.55 * Estimated flow at the Rio Salado gage), 14 where all three
units are measured in acre-feet per year. This historical relationship was used to characterize the Law of
the River that governs future Project releases from Project storage.
Water Use Patterns from Elephant Butte Releases. The ratio of Elephant Butte Irrigation District (EBID)
to Texas diversions is 0.567742 to 0.432258, taken from flows below Elephant Butte minus conveyance
losses and the Mexican delivery. New Mexico diversions are used entirely for irrigated agriculture.
Groundwater pumping supplements surface supplies. Texas water is used by El Paso area agriculture and
El Paso M&I. The ratio of agricultural to M&I diversions decreases with time due to increasing M&I
demand, and corresponding water purchases from agricultural uses. M&I also utilizes pumped
groundwater, while El Paso agriculture has no significant groundwater backup. Mexico
15Reclamation calculates a mass balance analysis to account for reservoir storage for Elephant Butte andCaballo Reservoirs. While the basic engineering formula above holds true: INFLOW = OUTFLOW + CHANGE INSTORAGE, as we have indicated above, evaporation is not the only reservoir loss that is individually accounted for inchange in storage. In order to account for unexplained losses in the mass balance analysis, Reclamation considersevaporation and other losses as two separate losses items. The other losses include bank storage effect and groundwaterseepage, particularly through the dam embankment.
16As Otowi flows increase, New Mexico owes an increasing percentage of these flows to Elephant Butte. Forexample, when Otowi flows are 1.1 million acre-feet per year, NM delivers 0.839 million acre-feet per year to ElephantButte. When Otowi flows increase by 0.1 million to 1.2 maf, NM deliveries increase by 0.1 million to 0.939 maf toElephant Butte. As Otowi flows increase above 0.939, NM owes more than 100 percent of the increase to ElephantButte. For example, when Otowi flows are 2.300 maf, NM owes 2.239 maf to Elephant Butte.
153
deliveries = 60,000 acre-feet per year (simplified interpretation of 1906 US Mexico treaty). Volume next
year at Elephant Butte = Volume this year + inflow minus (release + evaporation). 15
New Mexico above Elephant Butte ReservoirInflows into Elephant Butte. Flows into Elephant Butte are a function of flows at the Otowi gage not
including San Juan Chama flows; the quadratic function summarizes the Rio Grande Compact tables that
states New Mexico’s delivery requirements to Elephant Butte as a function of Otowi gage flows. 16
Albuquerque Area M&I: Albuquerque pumping depletes river flows by an amount estimated as a
function of lagged past pumping over the past four decades (Cook and Balleau 1998). Given past and
project demand patterns, this results in river depletions of about 60% of current pumping levels.
Albuquerque currently returns 60,000 acre-feet per year to the river from wastewater treatment plant. In
future years, Albuquerque will continue to return an amount to the river in acre-feet per year equal to the
current ratio of return flow to total supply of 0.41. Albuquerque’s M&I use will be supplied totally from
groundwater pumping for the next 10 years. Albuquerque’s total diversion of surface water will be
97,000 acre-feet after it fully develops its surface treatment facilities, assumed to occur by 2010. These
diversions include a senior right to a net water use (diversions plus pumping induced groundwater use,
minus return flow) of 48,200 acre-feet of San Juan Chama rights, with additional diversions having equal
priority to New Mexico (MRGCD) diversions for irrigated agriculture.
154
Rio Grande Bosque. Riparian use at the Bosque averages 255,000 acre-feet per year, with 195,000 acre-
feet per year above San Acacia, and 60,000 acre-feet per year between San Acacia and Elephant Butte
Reservoir. Bosque use, or riparian depletions, are represented as an increasing function of lagged river
flows. The function captures Bosque use of shallow, river-flow-dependent groundwater, which reduces
use in low flow years, while increasing use in high flow years.
Middle Rio Grande Conservancy District (MRGCD). MRGCD is the dominant water diverter in New
Mexico above Elephant Butte Reservoir. Future Albuquerque area population growth and its planned
surface water treatment development will increase net river depletions at the expense of some current
MRGCD’s surface water use. We would expect that Albuquerque will enter the water rights or water
purchase or rental market as a buyer of MRGCD water. MRGCD currently has essentially zero
groundwater pumping capacity.
ColoradoDeliveries to New Mexico. Water Colorado delivers to New Mexico at the Lobatos gage is a function of
headwater flows in Colorado. These headwater flows, called Index flows for the Rio Grande Compact
include three Conejos River Index gages plus the Rio Grande gage near Del Norte.
Use for Colorado Agriculture. Any water not delivered to New Mexico is available for use by Colorado
agriculture.
San Luis Valley Closed Basin Project. Deliveries to the Lobatos gage can occur from pumping from the
San Luis Valley Closed Basin project.
Relation Between Aquifer and Surface Water Use. When the aquifer level in the San Luis Valley is low,
Colorado’s water is used partly for crops and partly for aquifer recharge. When its aquifer is full,
Colorado’s water is entirely used for crops. Equations are written in the model to summarize annual
flows at the Lobatos gage and water available for use by Colorado agriculture as a function of the Index
flows described above.
155
Integrated Model for Institutional Response to Drought in the Rio Grande Basin
SummaryAn integrated model of the Rio Grande Basin (RGB) was developed to bring the work on
hydrology, economics, and institutions within a single framework. The RGB model is used to estimate
hydrologic, economic, and ecological impacts of a prolonged basin drought. Proposed alternative water
management institutions for minimizing drought damages are simulated using the RGB model. The
model is then further utilized to explore the sensitivity of assumed parameters of critical physical
linkages (e.g., surface-groundwater interactions) to the estimates of drought damages.
The integrated framework provides a flexible environment for representing alternative drought-
coping institutions. At the same time, the framework plausibly accounts for a set of physical interactions
between uses (e.g., agricultural, municipal, instream, and environmental), storage (including
groundwater), flows (including diversions, pumping from groundwater, and return flows), and various
losses (including field, canal, and conveyance losses). Because of the importance of interstate and
international water policy issues, relevant compacts and decrees, uses, storage, and flows must be
represented.
Existing models were not available to meet this need. Given the inability to examine the
effectiveness of alternatives institutions with existing tools, a fully integrated RGB model capable of
representing interactions between uses, storage, and flows within a flexible institutional environment was
developed.
BackgroundThe basin-wide RGB model structure builds upon similar integrated models previously used to
evaluate basin-wide water policies (e.g., Oamek 1990). Such approaches have also been used to integrate
instream uses, and water quality impacts (e.g., Ward and Lynch 1997; Lee et al. 1993). Water budgets
156
define the geographical structure in these models, while optimization of an objective function serves as
the driver. Objective functions may be chosen to replicate existing institutions, or may represent
alternative water allocation rules. Certain allocation rules such as minimum required instream flows can
be added as constraints. The model is written using GAMS 2.50, utilizing its integrated development
environment. Model solutions are estimated using the MINOS nonlinear solver.
HydrologyThe RGB model is a water accounting model with mass balance of surface and groundwater at its
core. Mass balance is developed for each node in the basin. Any given node may represent a river reach,
a consumptive use location, or a storage location such as a reservoir or aquifer.
Approach All nodes are measured in net flows of water per unit time, or consumptive use per unit time, or
storage volume in a given time.
Mass balance requires that for any node i,
�Yi (t) = yij(t) - xi(t) (3.42)j
∑
where �Yi (t) is change of storage volume Yi ; yij(t) is net inflow to node i from all nodes j,j
∑
and xi(t) is consumptive use at node i.
In the Rio Grande Basin, considerable time lags can occur in water transport between nodes. For
example, aquifer return flows to the river critically impact minimum flows, particularly in winter, but
157
occur over a time period longer than the anticipated time-step for implementation of this modeling
framework. Inflows to node i are thus defined by
yij(t) = dji yji (3.43)t∑
where dji summarizes the lags in outflow delivery yji from node j to i. For the special case where there is
no lag in flows at all, dji = 1 where s = 0, and �ji = 0 for all s > 0, which means yji (t)=yji(t). The approach
is described by Fredericks, and others (1998) in their use of time-lagged depletion and return flows.
Detailed ImplementationSeveral important surface and groundwater interactions are represented in the model. Each are
discussed below.
Surface Diversions for Consumptive Use. Diversions immediately reduce surface flow and are used to
produce economic and/or ecological benefits. Through seepage losses both in conveyance to a
downstream node and at the point of use, diversions typically increase storage in and availability of
groundwater resources. Unrecoverable losses to evaporation or saline aquifers may also occur. Surface
diversions are limited both by physical availability, and by institutional constraints such as the Rio
Grande Compact or surface water diversions established by water rights under state laws.
Groundwater Pumping for Consumptive Use. Groundwater may be directly used to produce economic
and/or environmental benefits. As with surface diversions, both recoverable and unrecoverable losses
may occur. Groundwater pumping is limited by physical availability and by groundwater pumping
permits established under state law.
158
Groundwater pumping limits reflect both available infrastructure, and the short-term possibility
of substantial drawdown or depletion of shallow aquifers during drought. The latter effect is captured
through a pumping limit that is a decreasing function of lagged river flows. The purpose of the functional
form is to capture decreasing ability to pump from shallow, river flow dependent, groundwater.
Pumping Limits. Pumping limits are set to determine the degree to which pumping would be scaled back
under sustained low-flow conditions. The parameter gamma is used, in conjunction with modeled river
flows, to determine the maximum level of pumping in any given time period. Coefficients are used with
modeled river flows to determine this pumping limit.
Water Use by Albuquerque. Albuquerque area surface diversions of its San Juan-Chama rights of just
under 50,000 acre-feet per year are limited in the model to those diversions leading to a net river
depletion by Albuquerque equal to these rights. Return flows accruing to the river increase diversion
rights, while the estimated depletions to the river resulting from pumping reduce the diversion right.
Groundwater Pumping by the City of El Paso. El Paso uses both surface and groundwater to meet its
M&I demands. In the model, El Paso is constrained to maintain a base level of groundwater pumping no
lower than the absolute level of 1999 pumping. Increasing future water demands are satisfied largely
from increased use of surface water.
Surface Water Use by El Paso. Surface water used by El Paso is provided out of the allocation of the
EPWID #1. Water users within the district are subject to the same allocation, and hence El Paso
municipal use of surface water is reduced proportionally to remaining agricultural uses in times of less
than full allocations.
Mexican Surface Water Deliveries. A constant 60,000 acre-feet annual delivery is assumed. Historically,
in times of severe drought, Mexican deliveries have in fact been reduced considerably below 60,000
159
acre-feet. Inspection of the data on Mexican deliveries show that a fairly simple regression relationship
could be estimated showing Mexican deliveries as a function of Rio Grande project releases in periods of
less than full supply.
Surface-Groundwater Interactions. Ground and surface water interactions are common throughout the
Rio Grande Basin. Groundwater may either contribute to surface flows producing a gaining river, or,
under other conditions, may remove water from river reaches resulting in a losing river. Past
groundwater levels are determined in part by past water use and river conditions. These groundwater
levels are modeled to determine the direction and magnitude of flows for a given reach and a given time
period. These interactions, including time lags, are represented in the RGB model using Equation 3.38.
Net gains or losses from groundwater return flows are a function of the lagged seepage from, or
depletion to, shallow tributary aquifers. Net seepage, the difference between percolation associated with
water use, and pumping depletions in the same aquifer, is used together with the lag structure to calculate
the net effect on river flows in any given time period. The lag is a simple linearly declining function of
net seepage. The lag time may vary from just the current year (no lag) to the full number of model time-
steps (years). The proportion of net seepage impacting river flows over the full lag ranges from zero to
one. For lags longer than the number of time steps to the first modeled period (e.g., a five-year lag in
model year 3), the net seepage in period one is used as a proxy for the missing periods.
Reservoirs. Reservoir accounting is used to determine reservoir storage, and direct economic benefits of
reservoir use. Accounting components are limited to inflows, outflows, and evaporation. Equations based
on reservoir levels characterize reservoir areas and hydropower head, allowing estimation of direct
economic benefits from recreation and hydropower, respectively.
Consumption by the Bosque. Consumptive use of water by the Bosque near Socorro New Mexico is
estimated using a simple physical model of local groundwater availability. The model uses a lagged
17The quadratic mathematical function approximates the lookup tables defined in the Compact, which relateupstream index flows (supplies) to downstream delivery requirements.
160
response function. The model represents consumptive use by phreatophytes whenever water is present in
the root zone. Bosque use, or riparian depletions, are represented as an increasing function of lagged
river flows. The purpose of the functional form is to capture Bosque use of shallow, river flow
dependent groundwater.
Inflows. The model reads a set of headwater inflows at six basin locations including water imports to the
basin from the San Juan-Chama interbasin transfer project. For the 50 and 100-year drought scenarios,
these inflows represent flows associated with the kind of drought expected to occur once in 50 years or
once in 100 years, respectively.
Consumptive Use of Water. Consumptive use is defined as the difference between surface diversions
plus pumped groundwater, and surface return flows plus deep percolation. The consumptive
(use defines the quantity of flows that are lost (through evapotranspiration, or simple evaporation) to any
future use by the system.
Mass Balance. Mass balance of all inflows and outflows occurs at each model node. Possible flows
present at a model node include inflows, diversions, surface return flows, groundwater return flows and
losses, bosque (riparian vegetation) depletions, reservoir evaporation losses, changes to reservoir storage
levels not including evaporation, and other uncategorized conveyance gains or losses supported by
historical relationships between pairs of nodes.
Compact Constraints. For purposes of this analysis, Colorado’s obligation to New Mexico under the Rio
Grande Compact, as described in the Compact delivery schedules, is captured by quadratic functions
defining the obligation given the Rio Grande and Conejos supply indices, respectively. 17 Departures from
the schedule result in debits or credits charged to Colorado. For this report, Colorado debits and credits
18Colorado has chosen to incur virtually zero credits and debits, but is not required to do so under the Compact.Under it, both Colorado and New Mexico are permitted annual and accumulated debits and credits. Article VI permitsColorado up to 100,000 acre-feet of annual or accrued debit and up to 150,000 acre-feet of annual or accrued credits.It permits New Mexico up to 150,000 acre-feet of annual debit and 200,000 acre feet of accrued debit and up to 150,000acre-feet of annual or accrued credits.
161
are set at zero in all years.18 New Mexico’s obligation to water users below Elephant Butte Reservoir is
approximated by a quadratic function defining required flows to Texas based on the Otowi supply index.
Departures from the schedule results in debits or credits, respectively, charged to New Mexico. Any
flows in excess of those that accrue as credits under the Compact are accounted for when New Mexico
cannot fully use its flows.
Water Distribution within New Mexico. Water use within MRGCD is assumed to be reduced
proportionally when necessary to meet Compact obligations. While this neglects the reality of senior
Native and acequia rights, it captures the reality that the dominant uses (by quantity) within the
irrigation district are likely to be treated similarly in times of water shortage.
InstitutionsMaximizing Beneficial Use
Institutions that allocate limited water based on economic value for each use, are frequently
proposed. Examples of institutions which are intended to increase the total economic benefits from all
water uses include water banking, dry-year options, and market transfers of water. In general, allocations
that maximize economic value at any time t can be found by maximizing the economic benefits function
(3.44)V t k tik
( ) ( , )= ∑ π
where �i (k,t) is the partial economic benefit produced by the k-th water use at time t.
A number of proposed institutions for operating the system, which vary from the status quo (Law
of the River) to a wide range of alternative institutions, can be accommodated with this approach. For
19Colorado and New Mexico have delivery obligations, Texas has none.
162
example, a regulated water bank with a set price can be modeled by adding a constraint on the price of
water in the solution to Equation (3.44). In practice water transfers or markets occur over a short period
of time. However Equation (3.44) can be modified to include the discounted sum of future benefits over
any desired time period, thus becoming a multi-period dynamic model.
Benefits from Consumption. Total benefits of water use are represented as quadratic functions of total
consumptive use, minus the net added cost per unit of consumptive use derived from pumped
groundwater rather than surface water. This is applied to both agricultural and M&I uses.
Benefits from Recreation. Recreation benefits are not derived from the consumption of water in the same
sense as agriculture or M&I users. These benefits are estimated as a quadratic function of reservoir
volume. The benefits function is based on the dependence of benefits on reservoir volume, which
depends of surface area.
Total benefits. Total benefits are the sum of benefits from consumption and benefits from recreation.
These benefits are summed over the 44-year time period of analysis.
The Rio Grande CompactThe 1938 Rio Grande Compact provides detailed use rights and delivery obligations for water by
Colorado, New Mexico, and Texas.19 The Compact specifies total annual flows to be delivered
downstream of major use points in Colorado and New Mexico, indexed to total annual flows upstream of
these points. The Compact divides annual flows among the three states at two points.
First, Colorado must deliver to New Mexico a minimum water volume based on the headwater
flows on the Rio Grande mainstream and the Conejos River. Colorado may use from 40% to 80% of
163
those total annual headwater flows, depending on those two rivers’ total annual production. Colorado’s
delivery requirements to New Mexico are measured at the USGS Lobatos stream gage on the mainstem
of the Rio Grande near the Colorado-New Mexico border.
Second, New Mexico must deliver annual flow to Texas at Elephant Butte Reservoir, defined as
a percent of annual flow on the Rio Grande mainstream at the Otowi gauge in northern New Mexico
downstream of the Rio Chama confluence. New Mexico may deplete between about 20% and 43% of the
Otowi flow, depending on total supply available. For Compact purposes, Texas is defined at the outflow
point of Elephant Butte Reservoir in southern New Mexico. Allocations downstream of Elephant Butte
are divided in fixed proportions between Elephant Butte Irrigation District in New Mexico (57%) and El
Paso Water Improvement District #1 Texas (43%). Table 3-50 describes allowed consumption of water
by state according to the Rio Grande Compact. Inflows originating in Colorado are in the first column.
These flows determine the use permitted by Colorado, and hence total flows that must enter New
Mexico. Currently most of the flow entering New Mexico is used for irrigation in the Middle Rio Grande
Conservancy District, and for uses downstream of Elephant Butte, (defined as Texas under the Compact),
including agriculture, and municipal and industrial uses.
164
Table 3-50. Water use apportioned by state under Rio Grande Compact, in 1,000 acre-feet peryear, exclusive of tributary flows produced in New Mexico and Texas.
Total Inflow
(Rio Grande at DelNorte, plus ConejosRiver near Mogote)
Colorado Use
(Based on totalCompact obligation at
Lobados)
New Mexico Use
(Between Otowi andElephant Butte, from
water delivered atLobados)
Texas Use
(Total delivery belowElephant Butte Reservoir;includes uses in southern
NM)
300 240 26 34
400 315 37 48
500 380 52 68
600 439 69 92
700 493 89 118
800 541 111 148
900 585 135 180
1000 624 162 214
1100 660 189 251
1200 692 217 291
1300 720 248 332
1400 745 278 377
1500 767 308 425
1550 782 323 445
1600 789 334 477
1650 794 352 504
1700 794 360 546
1800 784 385 631
1900 784 399 717
2000 784 405 811
Water RightsWe treat water rights as having the characteristics of a water production function. In particular,
for any given water right holder, the production function relates the actual water delivery over a given
period (wet water) to the sum of river basin inflows. While the sum of all off-stream deliveries will
increase roughly linearly with basin inflows (ignoring return flows and system losses), it is unlikely that
20For discussion here the The Mexican Water Treaty of 1906 (the "Treaty") is included. The Treaty regulatesthe flow of the Rio Grande between the United States and the Republic of Mexico, requiring delivery of 60,000 acre-feetper year to Mexico.
165
a given water right holder will experience constant returns to basin inflows. Rather, the user (e.g., a state
or nation) may be allowed decreasing (junior right) or increasing (senior right) marginal returns to basin
inflows. The case of constant marginal returns is that of a proportional right. This concept of linking the
seniority of a water right to the nature of the incremental flows reserved with increased total flows offers
insights into characterizing water rights implicit in compacts and treaties. This concept is particularly
helpful where, as is the case with the Rio Grande Compact, the text of the agreement provides little
intuition as to the nature of the respective state water rights.
Compact Delivery RequirementsAllocations under the Compact20 can be represented using a deterministic model. Central to the
Compact are a set of supply indices specifying the proportion of inflows to one sub-basin that are to be
passed to the downstream sub-basin. First, Colorado must deliver to New Mexico a minimum water
volume based on the headwater inflows. Let i(Zi) and Zi represent the supply indices and the headwater
flows, respectively, for Colorado, and let XCol represent the implicit consumptive use allocated for
Colorado of 40% to 80% of the total annual flows. Then
XCol = �i (1 - �i(Zi)) Zi. (3.45)
This equation says that Colorado’s consumptive use of water is one minus the proportion of
headwater flows that Colorado delivers to New Mexico under the Compact times that headwater flow. If,
for example, the headwater flow is 1,000,000 acre-feet and Colorado must deliver 0.376 of that flow to
New Mexico, then Colorado is allowed to consume, through its agricultural water use, (1 - 0.376) times
1,000,000, which is (0.624) times 1,000,000, or 624,000 acre-feet.
166
Next, New Mexico must deliver annual flows at Elephant Butte Reservoir for water users in
southern New Mexico, Texas, and Mexico. For New Mexico above Elephant Butte Reservoir (NM1), its
right to consume water under the Compact, XNM1, is defined by the supply index applied to Otowi gage
flows, labeled �i. This supply index �i can be applied to original headwater flows, Zi. Finally, New
Mexico can consume water from tributaries that enter downstream of the Otowi gage, and also imported
water. This means that
XNM1 = (1 - �(�i(Zi) (Zi) ) (�i �i(Zi) Zi) + Zexempt (3.46)
where Zexempt are tributary inflows including San-Juan Chama imports that can be fully consumed in
New Mexico above Elephant Butte. The river reach of greatest concern for the endangered silvery
minnow lies downstream of (most of) these uses. The factor 1- � indicates the proportion of Otowi gage
flows that New Mexico above Elephant Butte can use, and ranges from about 20% at high flow levels to
a maximum of 43% at low flows.
Downstream of Elephant Butte, water deliveries to Mexico (XMexico) of 60,000 acre-feet per year
must be made from the deliveries below Elephant Butte. With a fixed amount of water available, the
remaining allocation available for use in Texas (XTexas) and in southern New Mexico (XNM2) is
XTexas = � �(�i(Zi), Zi) �i �i(Zi) Zi - XMexico (3.47a)
XNM2 = (1 - �) �(�i(Zi), Zi) �i �i(Zi) Zi - XMexico (3.47b)
respectively. The proportion of Rio Grande Project water allocated to Texas, � =43%, and to New
Mexico, (1- � )= 57%, is independent of total flow, which means these two proportions are the same in
wet or dry years.
167
Institutions SelectedSeveral alternative institutions for managing basin water resources were modeled, described
more fully in the subsequent Policy Analysis section. These are used to introduce the range of
adaptations to drought in the basin and the resulting economic benefits or losses of various of alternation
adaptations. Institutions range from "business as usual," current basin water resource management,
through increasingly significant changes to existing regional water allocation institutions. To better
understand the potential benefits of within-state management changes, an "unconstrained" institution
allocating water to its highest economic use across all states and users, independent of the Rio Grande
Compact or other institutional requirements, was selected.
ReportingCalculated hydrologic, economic, and ecological impacts of alternative management institutions
under drought are reported by the model.
Impacts are presented for each modeled time-step, river reach, and economic and ecological
sector. Reservoir conditions are also reported. Aggregated reports are presented for state and sector (e.g.,
agriculture) levels of water use and the resulting economic impacts. Aggregated reports provide both
annual impact estimates, and total (present value) impacts calculated across all drought years.
DiscussionA modeling framework, the Rio Grande Basin model, for investigating alternative approaches to
drought mitigation in a three-state river basin is presented. The model provides a basis for understanding
drought impacts, identifying hydrologic and economic impacts of alternative water allocation
institutions. The Rio Grande Basin model provides a structure in which to investigate critical
groundwater and surface water linkages in the basin. The model characterizes the Law of the River by
assuming compliance with the Rio Grande Compact. Water reallocations under a number of alternative
institutions are modeled as the institutional adaptations for reducing the cost of drought impacts.